However, the Brazilian midfielder believes he can still regain the form that made him the world's best player in 2007.
The 30-year-old was left out of the Spanish champions' squad for their Super Cup victory over Barcelona and has yet to appear in the team in La Liga this season.
AC Milan tried to convince Real Madrid to loan Kaka back to them, but the Spaniards were only prepared to make a sale, given that they paid the Italian side around 65 million euros for his services three years ago.
The transfer window closed on Friday, and Kaka will have to stay at Real Madrid at least until January, with competition for his midfield place increasing following the arrival of the Croatian Luka Modric from Tottenham Hotspur.
Seemingly undeterred, Kaka, 2007 FIFA World Player of the Year when he inspired AC Milan to the Champions League title, says he is putting in extra training to try and win back Mourinho's trust.
"It's as if I was starting again at 30, after having won everything I've won," the player told TV Globo in an interview at Real Madrid's training complex, broadcast on Sunday.
"I even ask myself, how much is all this effort worth it. Wouldn't it be better to go somewhere else or even another, less competitive league? Well, the answer has been 'yes, I still want this (Real Madrid)'," he said.
"I arrive before the other players, do separate training, practice with the squad. The only way I'm going to get another chance is training more than the others and that's what I've been doing.
"Little by little the fans lost their hopes but I haven't lost hope yet and I believe I can still do a lot of good things at this club."
Kaka's move to Madrid was overshadowed by the signing of Cristiano Ronaldo shortly afterwards.
A series of injuries, including ankle surgery after playing for Brazil at the 2010 World Cup, added to his difficulties at the club.
Now he says he does not train with the idea of being a part of the starting 11, rather just to be a part of the bench.
"Today, I don't want to be a first team player, just to be in the squad (for matches)," he said.
The player denied Spanish media reports that he had rowed with Mourinho over his position at the club, and said the coach had promised him he would get a chance of a comeback.
"We have a professional relationship, of mutual respect. I think that in a squad it's normal for a coach to trust one player more than another...
"(Mourinho) made it clear that if I stayed at the club he would respect me and I'd have the same opportunities as everyone."