The Danish outfit succumbed to a 2-0 defeat at the Parken Stadium on Tuesday, meaning they can no longer reach the Europa League via a third place finish in Group B.
Real took the lead in the first half with a superb curling effort from Luka Modric to spark life into a lacklustre opening.
Delaney thought he had equalised when he had the ball in the back of the net in the first half, only for his effort to be chalked off for an apparent hand ball.
And the game was put beyond all doubt as Cristiano Ronaldo scored his ninth goal of the group stages - a Champions League record - shortly after half-time.
The Portuguese star had the chance to double his match tally from the penalty spot after being fouled by Delaney in the area in the closing stages, but the forward saw his effort saved by Johan Wiland.
Delaney said he believes Copenhagen produced a better showing in the second half and rued their inability to find a breakthrough.
"In the first half we felt that we were up against a much stronger opposition," he said.
"However, I think we managed to improve in the second half, where we were better at closing them down, and all we missed really was a goal."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.