Koskinen was pulled after Jeff Carter made it 3-0 at 13:57. It was the third even-strength goal in the past 42 games for Carter.
The Kings had scored 22 first-period goals coming into the game, second-fewest in the NHL behind the Dallas Stars.
"We didn't compete, so this is on everybody," Hitchcock said. "Everybody. When you have one player that competes at a high level in a game like this it can't be acceptable. There's been too much of this going on in the first 41 games. We win one and then we take our foot off the gas, and that's exactly what we did."
Kopitar increased the lead to 4-0 at 10:15 of the third period. He joined Luc Robitaille, Marcel Dionne, Dave Taylor and Bernie Nichols in scoring 300 goals for the Kings.
"I was hoping it was going to come a little bit earlier than that, but it's here and I'm pretty proud of that," Kopitar said.
Kopitar retrieved the puck at the end of the game for Quick, who is the 36th goalie in NHL history with 300 wins and is tied for 25th in NHL career shutouts.
"I didn't realize it until the very end," Kopitar said of Quick's 300th win. "It's great for Quickie obviously, and he's in my mind the best goalie in the world. It's very comforting to have him back there and a privilege to play in front of him."
