Crosby thought he tied it at 18:24 when a pass from Jason Zucker redirected off his skate, but video review determined the puck hit the crossbar and trickled along the goal line without going in.
"It just didn't seem to want to go in," Crosby said.
Tristan Jarry made 20 saves for the Penguins.
Despite the result, their new teammates said they were pleased with how Marleau, Sheary and Rodrigues fit.
Sheary, who was acquired along with Rodrigues from the Buffalo Sabres for forward Dominik Kahun, was minus-1 in 18:14 of ice time. He was used on the top line with Crosby and Zucker to begin his second stint with Pittsburgh, where he played his first three NHL seasons and won the Stanley Cup in 2016 and 2017.
Marleau, who was acquired from the San Jose Sharks for a conditional pick in the 2021 NHL Draft, had one shot in 14:29. Rodrigues won four of five face-offs and played 7:48 while centering the fourth line.
"Those guys were great. I think you can see what makes them successful players in the League," said Penguins forward Bryan Rust, who scored on a backhand shot after a pass from Evgeni Malkin at 6:42 of the third period for the 2-1 final. "Obviously a lot of us are familiar with Conor and even playing against [Marleau] in the playoffs, I think we know how good he's been for so long. Rodrigues came in, [and] you could see how hard he works and his wheels and just the team game."