The Tyneside outfit were thwarted by a string of fine saves from Costel Pantilimon, before Alvaro Negredo and Edin Dzeko struck to seal City's passage to the quarter-finals.
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"If that goes in it could've been different," said the Newcastle boss. "I think it was obvious the first goal would be crucial and they got it.
"David Silva had a big influence when he came on but before that I thought we were the better side.
"I'm disappointed for the fans and our players because they put on a terrific show after the disappointment of Sunday [losing to rivals Sunderland].
"It was just a shame we couldn't get the goal we deserved."
City striker Dzeko, who set up Negredo's opener before scoring the second himself, said the match was a good chance for fringe players to prove themselves and lauded the performance of Pantilimon.
"Tonight was a chance for those of us who maybe haven't played in the last few games to show the manager we deserve to play," Dzeko told Sky Sports.
"We have to show it on the pitch and I think we did that tonight.
"He [Pantilimon] was great. He's working hard in training and that is now the second game in the cup where he hasn't conceded a goal, so he's improving."