Bruce's side were superb in the first half and should have taken the lead as Sone Aluko went through on goal, but the Nigeria international could only scuff wide when one-on-one with Joe Hart.
They also looked solid at the back, but as the hosts ramped the pressure up, Alvaro Negredo nodded his team in front after the hour, with Yaya Toure adding a gloss to the scoreline with a stunning late free-kick.
However, Bruce - who also saw his side go down 2-0 at Chelsea in their first game of the season - was heartened by his side's showing against one of the favourites for the Premier League title.
He said: "We couldn't have asked for more really. Our Achilles heel in the championship last year was 'can we score enough?'
"Certainly we've got really good players, and we've added to that, and you can see why we've come out of the Championship with the way we played. But we need to score.
"I've been here a few times since the change - I think I've had more chances today than I've had in six games against them so we needed to take one.
"But overall I'm very, very pleased."
The former Sunderland and Wigan boss saw Danny Graham’s first-half strike chalked off for offside and, although Bruce admitted the decision was correct, he was left to rue his side not getting the rub of the luck.
He said: "The linesman gives an offside, which he's right, but he’s two inches offside
"I thought these days (the benefit of the doubt) was supposed to go to the attacker, but when you see it and you realise how close it is it’s a big call.
"You need that little bit of luck when you come here but it wasn't to be."
