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The Black Cats produced an assured display against the Red Devils and were deemed the better side in the match.
"The performance was terrific I couldn't have been more pleased with it. That's eight points we've taken now from the top teams," Bruce told Sunderland's official website.
"It's been hard work and it's been hard fought and we've only got eight points from it. On another day we might have got more, but I'm really pleased with the result and of course the performance.
"We had plenty of chances and we've got to start taking these chances. We can't keep relying on Darren Bent or Asamoah Gyan to score, that's the only critical thing I could say, that we didn't take our chances.
"Manchester United are always a threat. Late on you're thinking please don't score, our performance doesn't deserve that.
"How many times do you see them score in the last five minutes, that's the type of team they are, a constant threat.
"Overall I'm delighted with the performance. It was well deserved."
United boss Alex Ferguson also acclaimed Sunderland after the match for their performance.
"I think you've got to give Sunderland credit, their home record this season is fantastic," he told Sky Sports.
"We've had to defend really well and that is the pleasing thing for me. The back four were fantastic."