The Tigers played their first Premier League game in over three years after sealing automatic promotion on the final day of last season, but were helpless as goals from Oscar and Frank Lampard sealed the three points for the Blues.
Bruce's men improved as the game went on but the former Sunderland boss admitted that Chelsea were just too good at times for the newly promoted outfit.
"The first 20-25 minutes was just unstoppable for us," he told Sky Sports.
"The intensity, the ground, the way it was - what a stark contrast to last season.
"The ground's right behind the new manager, the players are all ready for it and when they play with that intensity and movement and fluidity, they were just a constant threat so we had to stick at it big style.
"Thankfully in the second-half, human nature makes you take your foot off the pedal a little bit and we were better then, but in the first half-hour, not many teams could live with that intensity so for us to stick at it was terrific."
Lampard's 30-yard free-kick was the pick of the goals, although Bruce thought that goalkeeper Alan McGregor, who had earlier denied the midfielder from the penalty spot, could maybe have done better.
"The one thing about this new ball, the likes of Lampard in particular, have got this way of kicking it where the ball moves all over the place," said Bruce.
"I'd like to see the actual free-kick because I didn't believe it was a free-kick but when Alan looks at it, he will be big enough to say he should've stopped that, maybe because of how far out it was but it was a wonderful strike."
Bruce handed debuts to recent signings Tom Huddlestone and Jake Livermore in the second-half, and he believes that the duo, who joined from Tottenham earlier this week, can have an important role to play this season.
"They'll make a difference to us, you can see that," he said.
"They've only been with us a couple of days, they'll get to know everybody and what we're up again and what we plan to do and they'll make a difference to us because we were certainly better when they two were on the pitch."
The Tigers welcome Norwich City to the KC Stadium next weekend, a game in which Bruce thinks that three points could be vital.
"We've got a big game next week, it turns into a big game. If you can take anything against the big boys, the one thing when you come to Chelsea or any of the big teams, you need them not to play well and you to play at your best," said Bruce.
"We had a rampant Chelsea who simply in the first-half we weren't good enough against. There's no shame in that, we understand that, that's why they play for Chelsea and they're top, top players.
"Our season will be defined against the teams who are going to be at our end of the table and that are where we're going to have to pick up the points."