Hull were 2-0 down after just nine minutes but fought their way back into the game with two goals in two minutes before the break.
Loic Remy’s late winner off the bench after 77 minutes meant Bruce’s side went away with nothing, but he insists Hull will stay up if they reproduce performances like that.
He told Sky Sports: “You’ve got to look at the performance first of all, especially after going 2-0 down after nine minutes.??
“The players have put in a hell of a shift, when I look back and analyse it, we showed we’re ready for the challenge that lies before us.
“We’ve played well over the last couple weeks and we’ve played well today. We’re just disappointed we didn’t take something from it.
“I thought we deserved something from it. If we keep playing like that we’ll be fine.”
Bruce rued Hull’s three missed chances with the game at 2-2 in the latter stages, Thibaut Courtois keeping out Ahmed Elmohamady, Jake Livermore and Gaston Ramirez in the space of a few seconds.
However, Bruce admits he has never seen his side put in that sort of performance since they were promoted to the Premier League in the summer of 2013.
“The big turning point is when we’ve had three chances in the space of ten seconds.??
“If you’re going to beat Chelsea you’ve got to take one of those chances. It’s a shame to lose a goal in that respect.??
“That’s probably the best performance we’ve produced in the 18 months we’ve been in the Premier League.”