Richards, who played for City between 2005 and 2015, expressed his concerns for City who showed a lack of hunger for much of the contest.
"It does hurt, but for me it doesn't really feel like a derby anymore," he said on Sky Sports. "There weren't that many challenges going in. City played possession football without creating too much.
"People will say it wasn't such an important game for City as it was for United, but to the City fans it is. This is a game that you want to win. Today I just thought we were a bit passive.
"I don't want to question the hunger but it's a derby, it's different. When you come from City, this is a big game, and tonight it didn't feel like that for me."