The former Manchester United man went on to say that PSG now have their sights set on lifting the trophy.
"It has been a very special day for many reasons. It is impossible to have a better performance and birthday. it was a wonderful display and we deserved the win," Di Maria told reporters.
"We controlled the game for 90 minutes. It is hard to control Neymar, Suarez and Messi but we managed it. We covered ground and worked hard. The big thing is the win and moving forward.
"Our aim is to reach the final and win the Champions League. We are getting there gradually. This was a game against one of the best teams in the world. There is still more to do at the Camp Nou. They will be quick out of the blocks. We will have to do the same as tonight and more."