City won after having captain Vincent Kompany sent off after just 10 minutes.
Bruce was left to rue his side's inability to make the most of their chance to build on last Sunday's FA Cup quarter-final win over Sunderland.
Bruce said: "I think the frustration is we have never had a better chance to beat them. In the end it became one of those frustrating afternoons.
"We know how difficult it is to play against 10 men. We needed the game to go 30 or 40 minutes longer before Silva scored - that gave them something to hang onto.
"It's been a difficult week for Manchester City but I have to say they defended fantastically well.
"We just didn't have the quality to break them down but I have to say City defended very, very well and they scored a wonder goal. Silva's was a fantastic piece of individual skill."
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