Despite being on the backfoot for large periods of the game, City came away with the three points courtesy of Edmilson Dove's 79th minute strike.
McCarthy even admitted that Chiefs could have put the game to bed in the opening half and that his side were flat, but was satisfied with his side's improvement in the second stanza.
"It was not one of our proudest performances," said McCarthy. "The first half we were a bit flat. Chiefs could have put the game to bed if I must be honest. They didn't look like a team that played on Sunday. It looked like they wanted it more.
"The half-time teamtalk seemed to work and then we came out and then we looked more like a team that's up for it. Then we began to string a few passes together and draw them out and try to find (Gift) Links and Craig Martin as we usually do.
"And then we started creating chances. If it was 0-0, both coaches would have been happy with a point. But the odd occasion you take a smash and grab. But the fight from my players was second to none. We keep ticking away and prefer to be the underdog."