"Bish is going to play again in this series, there's no question," he said. "I just don't know which game."
Bishop did not take pregame warm-ups Wednesday. Instead it was 20-year-old rookie Andrei Vasilevskiy who led the team onto the ice at United Center.
Vasilevskiy, in his first NHL playoff start, made 17 saves in the loss, which knotted the finals at two games apiece. He became the fourth-youngest goalie to start a Stanley Cup finals game in NHL history and the youngest since 20-year-old Patrick Roy in 1986.
"I can play under pressure," Vasilevskiy said. "For me, it's not something new. I was ready for pressure from fans and players."
Bishop was not available to back up Vasilevskiy, either. Kristers Gudlevskis took that spot instead. The 22-year-old Latvian Olympian spent this season in the AHL and has just three games of NHL experience, none this season.
Cooper was impressed with Vasilevskiy's performance.
"If you tell me we're going to come in and he's going to give up two goals, that's a hell of a job in my book," Cooper said. "That kid gave us every chance to win the hockey game. We only scored one. ... He showed at the pinnacle of the sport that he can play. That's a pretty big achievement for a 20-year-old."
Bishop, 28, has been battling through the undisclosed injury. There was speculation he would not play in Game 3 but he gritted through Tampa Bay's 3-2 win Monday night, although he appeared to be laboring almost the entire night.
Game 5 is Saturday night in Tampa.
Vasilevskiy previously appeared in Game 2 of the series, stopping five shots in relief of Bishop when Bishop exited the game on two separate occasions.
Vasilevskiy joined the Lightning in December and played in just 16 games during the regular season -- none since March 31 -- before mopping up in two playoff games. Yet the likable Siberian has been touted as one of the greatest Russian goaltending prospects of recent years, earning comparisons to Vladislav Tretiak and winning a gold medal while backing up his idol, Sergei Bobrovsky, at last summer's world championships.
ESPN.com's Pierre LeBrun and The Associated Press contributed to this report.