Blues dominated proceedings in their first home game of the season against Jose Mourinho's side but the performance proved fruitless as Joe Coles deflected shot 20 minutes from time saw Chelsea leave St Andrews with all three points.
"I could not be any more prouder with the performance, they were fantastic, against a side that will without doubt be one of the top three sides," Bruce said after the game.
"The one thing that does upset me though is that when you get to this level you've got to have a cutting edge to stick the ball in the back of the net. Unfortunately we just didn't have that today and its proved a big blow to us.
"We outpassed them and we created the better chances but in big, big games like today you need that steely resolve to put the ball in the back of the net and unfortunately we didn't do that.
"Its not very often that when you lose the fans cheer you off the pitch and I think they realised that we gave it all that we can."
"I could not be any more prouder with the performance, they were fantastic, against a side that will without doubt be one of the top three sides," Bruce said after the game.
"The one thing that does upset me though is that when you get to this level you've got to have a cutting edge to stick the ball in the back of the net. Unfortunately we just didn't have that today and its proved a big blow to us.
"We outpassed them and we created the better chances but in big, big games like today you need that steely resolve to put the ball in the back of the net and unfortunately we didn't do that.
"Its not very often that when you lose the fans cheer you off the pitch and I think they realised that we gave it all that we can."