The winger denies he was forced out of Stamford Bridge by former Blues boss Mourinho, but he admits the time was right to move on.
Robben told the Sunday Mirror: "When I look at the way things went at Chelsea in the last year, it was not a nice time for me. Sometimes we played 4-3-3, sometimes it was 4-4-2.
"That made me rage with anger. Thank God he put me on, and I was able to be decisive for the team. That lifted my spirit a tiny bit. But when I think about most of our Champions League matches, I get fed up. We were always playing so defensively, there was no room for me. In the end I had just had enough. I wanted to play football again. At Real I am more important as an attacker."
Does Robben bear a grudge against Mourinho after everything that has happened? He said: "I've become a stronger player mentally. Whatever has happened, I do admire Mourinho for the fact that he is a top-class coach.
"I learnt a lot from him. The way he works with players, the way he thinks about football - it is all very impressive and every player must have learnt from Mourinho's coaching at Chelsea.
"But in the end it is not Mourinho who improves you as a player. I improved myself. Mourinho decided the tactics and the line-up for each match, but it is up to each player to be of more value for the team.
"I just treasure all the good moments I had at Chelsea and I forget the rest."
Robben says he has not spoken a word to Mourinho or any of the Chelsea players since he left in a hurry.
"I hardly spoke to anybody at the club. I do regret that. I would have liked to say goodbye properly to a lot of people. But it all happened in a big rush.
"On the Wednesday I heard there was a deal between Real and Chelsea, on the Thursday I was on a plane to Madrid.
"Even if I had wanted, I could not have said goodbye.
"I have always had a good rapport with the fans. This is why I wrote something in the match programme the other day. I wanted to thank them for supporting me in bad times or when I was injured.