The Premier League outfit managed to prevent Real Madrid from scoring in the first leg of their Champions League semi-final at the Etihad, but could not find the back of the net themselves as it finished goalless in England.
Kompany has conceded that it will be "very difficult" for his team in the second leg at the Bernabeu, but refused to be disappointed with a goalless draw against the 10-time winners.
"It will be a very difficult game. A 0-0 is a good result. It's hard to keep a clean sheet against such a good attacking team. We can be proud of what we've achieved in this first leg," Kompany told BT Sport.
Real Madrid were without the services of Cristiano Ronaldo on the night after the Portuguese aggravated a thigh problem in training.