But Sander Berge’s injury-time header helped to lift Sheffield United’s spirits.
“Should have been a clean sheet, could have been more goals but this is football, this is the play-offs,” said Cooper, who took over in September when the Reds were in the Championship relegation zone before overseeing a fourth-placed finish.
"It was a really good game, I loved our first-half performance – dominant. I was really impressed with out mentality and our approach to the game.”
Cooper added: "Whether we like it or not these games are different.
"To come to a big stadium like this, against a good team, good players, good atmosphere and to do what we did tells you our mentality is in a good place.”
Forest managed eight efforts on target to United’s three – and perhaps should have established a greater lead in the match by half time.
Cooper said: "They had a bit more of the ball than probably what we would have liked and what it normally looks like in our games, in the second half.
"We also knew if we got our defending right we’d continue to create chances, which we did, and got the second.”
He added: "It’s disappointing to concede at the end but that’s the tension and the randomness of the play-offs.”