The loss eliminates the U.S., which was looking to follow up on a bronze medal won at the Worlds last year, while the Czech Republic moves into the semifinals Saturday against Finland.
The United States last won consecutive medals at the World Championship in 1933 (gold) and 1934 (silver).
"I'm disappointed that our tournament stops here but I'm proud of the way we played," U.S. coach Peter Laviolette (Predators) told the IIHF website.
The goals by Hertl and Cervenka gave the Czech Republic a 3-1 lead and came after a five-minute penalty for charging and a game misconduct were assessed to U.S. captain Justin Abdelkader (Detroit Red Wings) for a hit that knocked Czech forward Vladimir Sobotka (St. Louis Blues) from the game 6:41 into the second.
It took the Czech Republic 10 seconds after the penalty to take the lead for good when Hertl converted the rebound of a Jiri Novotny shot. Cervenka thought he had made it 3-1 about 20 seconds later, but his goal was disallowed because it was ruled he had kicked the puck in. However, he cleaned up the rebound of a Jan Kolar shot at 8:06, beating U.S. goalie Tim Thomas (Dallas Stars) for a clean goal.
"The turning point was obviously when their captain took the penalty and we were able to score two goals," Czech Republic coach Vladimir Ruzicka said. "After that we focused on our neutral-zone trap and most of the time we did that OK."
Ruzicka added he was hopeful Sobotka would be able to play in the semifinal round.
Forward Ondrej Nemec extended the Czech lead to 4-1 at 16:19 of the second, and that goal turned out to be the game-winner after U.S. forward Tyler Johnson (Tampa Bay Lightning) scored twice in 13 seconds in the waning moments. Johnson converted what essentially was a 6-on-4 goal with 1:10 left, one second after a penalty to Czech forward Jacob Klepis expired, and then added another extra-attacker goal with 57 seconds remaining. But the U.S. couldn't put another puck past Alexander Salak, who finished with 31 saves.
"I think we did as well as we could have done in the last minute there, getting those two goals," Johnson said. "We had some chances and we had to bury one. I think that shows a lot of character, but I wish it had come a little sooner.
"In the end it was a good game. Those five or seven minutes, whatever it was, when we were in penalty trouble and they got those quick goals, that's what really killed us in the end."
The teams traded goals in the first period. Brock Nelson (New York Islanders) scored on a power play at 6:54 to open the scoring for the United States, but the lead was short-lived as Czech captain Tomas Rolinek scored unassisted at 9:25 to even things up.
Finland 3, Canada 2: Iiro Pakarinen scored with 3:08 remaining as Finland eliminated Canada with a 3-2 win Thursday in the quarterfinals of the 2014 IIHF World Championship in a game played at Chizhovka Arena in Minsk, Belarus.
Olli Palola and Juuso Hietanen also scored and Pekka Rinne (Nashville Predators) stopped 36 shots for Finland, which will face the Czech Republic in one of two semifinals scheduled for Saturday.
"We got a good start in the first period, but in the second period Canada was very strong," Finland coach Erkka Westerlund told the IIHF website. "In the third period we found the mental strength. We call it 'sisu' [in Finnish]. I am very proud of my team."
Kyle Turris (Ottawa Senators) and Mark Scheifele (Winnipeg Jets) scored second-period goals for Canada, which lost in the quarterfinals for the fifth straight year. Canada last medaled at the Worlds in 2009 (silver) and hasn't won gold in the tournament since 2007.
Canada won gold at the 2014 Sochi Olympics and was bidding to become the second team, following Sweden in 2006, to capture gold in the Olympics and the World Championship in the same year.
"For the most part I thought our team played well," Canada coach Dave Tippett (Phoenix Coyotes) said. "We controlled long portions of the game. We made a couple of mistakes that cost us the game. Our goal was to get better every day. That was probably the best game we've played here."
Canada had won six in a row since losing to France in a shootout in its opening game in the preliminary round, and led 2-1 starting the third. Hietanen got Finland even 28 seconds in, beating Ben Scrivens (Edmonton Oilers) with a shot that hit his blocker and trickled across the goal line.
Pakarinen scored the game-winner after Jori Lehtera, who assisted on all three Finland goals, took advantage of a turnover by Canada defenseman Tyler Myers (Buffalo Sabres). Lehtera fed Pakarinen for a shot that beat Scrivens between the pads.
Finland improved to 8-34-2 all-time against Canada at the Worlds.
Turris pulled Canada into a 1-1 tie at 5:41 of the second when he completed a give-and-go with Matt Read (Philadelphia Flyers) by firing a shot past Rinne on the glove side. Scheifele scored unassisted at 12:08 off a 2-on-1 rush after stripping Petri Kontiola of the puck.
Palola opened the scoring in the first on a Finland power play. Myers was in the box for roughing when Palola one-timed a Lehtera pass and beat Scrivens at 6:14.
Finland took four minor penalties in the opening 20 minutes but killed them all, as Brayden Schenn (Flyers) and Nazem Kadri (Toronto Maple Leafs) hit posts for Canada.
Russia 3, France 0: Evgeni Malkin (Pittsburgh Penguins) had a goal and an assist while Alex Ovechkin (Washington Capitals) was scoreless in his return after missing one game due to injury.
Sergei Bobrovsky (Columbus Blue Jackets) stopped all 16 shots he faced, and Russia also got goals from Artem Anisimov (Blue Jackets) and Alexander Kutuzov to advance past France in a game at Minsk Arena.
Russia, which was the only undefeated team in the preliminary round (7-0), advances to the semifinals Saturday to face Sweden, which beat Belarus 4-2 in another quarterfinal game.
Anisimov started the scoring at 4:21 of the first with a wrist shot that beat France goalie Cristobal Huet. Malkin doubled the lead 52 seconds into the second period on a power play.
"I felt much better [Thursday]. I had the time to get acclimated," said Malkin, who didn't join Russia until after the second round of the Stanley Cup Playoffs. "[Nikolai] Kulemin (Maple Leafs) and I have played with each other a lot before and I know how to play with him. It's very comfortable for me on the line with [Kulemin and Viktor Tikhonov]. It was a good win, but we could have played better and been more effective."
Huet kept his team within striking distance and France killed off a 54-second 5-on-3 advantage for Russia in the second, but Kutuzov finally put the game away 7:36 into the third with a one-timer off a Malkin feed.
Ovechkin sustained an injury to his right leg during Russia's preliminary-round game against Germany on Sunday, but an MRI revealed no ligament damage to his right knee. He sat out Russia's final opening-round game, Tuesday against Belarus, but practiced Wednesday and took regular shifts against France on Thursday, wearing a knee brace.
"Of course it was a bit awkward to skate in the brace," Ovechkin said. "But I think I'll play without it the next game and everything will be OK. I wasn't risking anything. I knew the brace would protect me in case of a collision. That's what happened in the first period and I immediately knew that the leg is reacting well."
Sweden 3, Belarus 2: Defenseman Mattias Ekholm (Predators) scored on a wraparound with 6:22 remaining as Sweden survived a staunch effort from host nation Belarus in a game at Minsk Arena and advanced to the semifinals Saturday, against Russia.
Less than a minute before he scored, Ekholm was called for hooking Belarus captain Alexei Kalyuzhny on a breakaway, leading to a penalty shot. Anders Nilsson (Islanders) made a stick save, one of 21 shots he turned aside.
Nicklas Danielsson and Jimmie Ericsson also scored for Sweden.
Geoff Platt and Alexei Yefimenko scored in the second period as Belarus took a brief 2-1 lead in its bid for an upset. Kevin Lalande made 22 saves.
Danielsson's power-play goal with 6:19 left in the first, off the rebound of Ekholm's point shot, got the scoring started. But Belarus came back strong in the second. Platt scored the tying goal at 5:39 and set up Yefimenko for the go-ahead goal at 14:14. Sweden responded at 17:27 on another power play, Ericsson tipping in a shot by Magnus Nygren.