Leeds, who were the better side in the first half and missed a number of chances at the City Ground, were sunk by Brennan Johnson's goal which helped drag Forest six points clear of the relegation zone.
The former Real Madrid goalkeeper, a three-time Champions League winner, made his debut following his deadline-day loan move from Paris St Germain and produced a number of good saves.
Cooper said: "You don't need me to tell you about his experience and about the success he has had in his career.
"He would still have wanted to do well for his new club in his first game for sure and he did.
"Brilliant in the first half, outstanding and composed. The obvious talking points are the saves, and rightly so, he deserves all the credit for that, but I loved his composure and game management and decision making, I really enjoyed that part of his performance.
"Delighted he has got up and running, it was something that helped us win for sure.
"We've had a good few days with him where all he's shown is a real good work ethic, humility, desire to jump on board. We are really pleased he is here and are looking forward to working with him."