Nuno Espirito Santo's side held on for a deserved victory, handing Newcastle their first loss under their new owners – and Bruce's 1000th match as a manager.
After the loss, Bruce bemoaned his team's defensive flaws, as the search for a first league win of the season continues.
“We were beaten by the better team after a wonderful start,” he told Sky Sports.
“Problems that we’ve had for a while now defensively were there for all to see unfortunately.
“We’ve started a few games like that, we’ve got off to a good start and scored, got our noses in front, unfortunately we’re not able to defend well enough as a team.
“From front to back at the moment, we’re not defending well enough. We’ve tried to change, to be more on the front-foot if that’s the right word you say these days, but it’s difficult because you get yourself having to score three goals to win a match.”