The Reds beat Tottenham 2-0 at the City Ground. Goals from Renan Lodi and Jesse Lingard gave Forest a passage into round four.
Forest were forced to sweat late on. Mangala was shown a second yellow card by referee Peter Bankes after picking up an earlier booking for a foul on Djed Spence.
Mangala was distraught with the decision. He will now miss the final game before the World Cup against Crystal Palace on Saturday.
Cooper had some sympathy for his player. After the game, he spoke to local radio and said it was almost the perfect night for the Reds.
He told BBC Radio Nottingham: “We know there is a really good player in there and he needs a bit of luck.
“He goes and runs the game tonight and then he’s unfortunate to get the yellow card that goes and rules him out of Saturday.
“It’s a sour note because it’s one step forward and then another step backwards.
“But we believe in him. He’s going to do well and contribute a lot here.”
Mangala will serve a one-match suspension. As a result, he won’t be available for selection on Saturday when the Reds take on the Eagles.
Cooper has sympathy for unlucky Mangala
Last night this proved the only sour note. Forest played brilliantly well and in truth, his second yellow card probably was a little bit harsh.
But, when you go diving in on a yellow card, there will always be a chance that the referee will feel he has the decision to make.
Forest were much better though. Tottenham only made three changes to their team and it was always going to be a stern test.
The Reds played tremendously well in the second half. In truth, they could have scored more goals than they did.
Mangala now has some time to get himself fit. Hopefully, during the second half of the season, he can roar back and earn a run of games.