The Bluebirds conceded to a fine Edin Dzeko strike in the 52nd minute but hit back through Aron Gunnarsson on the hour-mark prior to a headed double from Fraizer Campbell before a late header from Alvaro Negredo gave the visitors hope.
After the match, former City striker Bellamy told Sky Sports 1HD that the overall team effort of the Cardiff side pleased him to no end.
"It was a tough afternoon for us, Man City are such a good football team," he said.
"We had to be patient, we knew we weren't going to have the ball for long periods.
"With Fraizer today, not just his second-half goals, but in the first-half he created a lot of opportunities for himself. When you're a threat you always feel like you have a chance of maybe nicking a goal.
"It was a great goal by Dzeko, Man City are capable of that. As well as we defended, all it takes is that one great strike which he hit.
"But we kept our heads up. That's the thing about our players as well, we'll keep going no matter what."