Dunne joined Villa from City in the summer and opened the scoring when the two clubs met at Villa Park on Monday.
The game ended in a 1-1 draw and moved City back into the top four in the Premier League.
The Republic of Ireland defender told ESPN: “I don’t have a celebration – when I score it’s usually a surprise.
“I really enjoyed my time at City and I really respect the club and the fans and [not celebrating] seemed the right thing to do.
“It just seems to happen playing against your former club, people seem to score. I wasn’t expecting to score tonight.”
He added: “Unfortunately we couldn’t go on from there and get the second.
“Manchester City are a real good team and they’re going to push the top four this season.
“We feel we’ve got as much chance as teams like Man City, Everton, Tottenham – we feel we’re as good as them.”
“It was difficult but I don’t think it was a case of holding out,” he said. “We had opportunities as well.
“After the goal the last 25 minutes was quite even so I think both sides would have been happy with a draw.”