Trailing 3-2 from the first leg, City faced an uphill battle at the Bernabeu but were undone by Madrid’s pace and precision.
Kylian Mbappe’s hat-trick sealed a 6-3 aggregate win for Carlo Ancelotti’s side, ending City’s European campaign.
“We were not good enough. Shake hands and we look forward,” he said post-game.
“We have a lot to improve, we have to be better. Football is like this.
“It’s the moment and you have to be good enough in the moment and if you’re not good enough in the moment then football takes over. It is what it is.
“Obviously, in our minds the disappointment is maybe heavier than usual because we don’t like to lose. We don’t like to be in this position. It’s not just that we’ve got used to winning every year, it’s just out mentality, it’s our way of being, it’s our air that we breathe.
“As such, it hurts more. We don’t take it lightly. The only way to improve and the only way to look forward is to accept what happened, and today we were not good enough.
“I say it without any problem, you have to accept it. It’s the only way to move forward and the only way to actually look at ourselves and realise that we have to do better. We were not better than them. As such they deserved to go through.”