Following the arrival of Belgian shot-stopper Thibaut Courtois, Navas was forced to the bench and to enjoy more game time, the Costa Rican secured a move to PSG on deadline day.
Winning the Champions League on three consecutive times with Los Blancos, many see his departure as being treated unfairly by the club.
But Navas, who joined Madrid from Levante has stressed he holds no grudges with the side he spent five years at.
"I am very happy because we won, not because we beat Real Madrid," Navas said.
"My team-mates put in a great effort, gave their best and we won, which is really important for us.
"I have no resentment towards anyone at Real. I just want to enjoy the moment I have here at my new club. Everyone is very motivated and I will defend my new colours as I did with Madrid.
"I want to continue writing my story. The one I lived in Madrid was very beautiful. I want to be happy here, enjoy every moment and for my family to be happy, that is the main thing.
"I did not leave Real Madrid because of that," he said, when asked about the rivalry with Courtois.
"I left because my family and I thought this was the best option for us. I was welcomed as if I had been here for a very long time.
"The best I can give is to defend these colours to the death, to work hard and to try to win important games."
Assisting in piling pain on his former side, Navas made several saves to deny Real from scoring as they defeated the White Angles 3-0 at the Parc de Princes on Wednesday thanks to a brace from Angel Di Maria and Thomas Meunier's late goal.
Joining PSG on a four-year contract, Navas made his second appearance for the side after featuring in 1-0 win over Strasbourg in the Ligue 1.
