Forest lost 2-0, with City midfielder Rodri seeing red immediately after halftime.
Cooper said: "We know who we're playing and the level that they play at and it's really difficult to prepare for and to obviously go and play.
"You're always disappointed with goals you concede, of course, it's something that they do so much with the ball with Walker running in behind and at the back post with Haaland we talked about it so much and if you concede with something that they do so often you want it to be with real difficulty and that wasn't really the case. It was done too easy.
"We're disappointed with that and the players will be disappointed with that as well.
"It can go both ways then when you're two nil down. To be fair to the guys they really stuck to the task and things changed obviously with the red card and then we became the team that was pushing and pressing.
"I would have liked us to have shown a bit more quality in the final third."