"I'm not disappointed in my relationship with Milan," he told reporters in the Brazil team hotel in Recife at a news conference broadcast live on television.
"There has never been a (financial) crisis like this one, I understand perfectly the club's position and I'm very grateful to Milan and the president," added Kaka, who joined the Rossoneri in 2003.
The 27-year-old has agreed to a six-year contract to join Madrid, which reports have said involves a transfer fee of around 68m Euro, the second biggest ever. Zinedine Zidane joined Real from Juventus for around 73m Euro in 2001.
"I've won everything that I wanted as a player and this is a new motivation for me," Kaka said.
"The club needed to make this sacrifice, and I understand this very well. I don't blame the club for this.
"Everything I've done for Milan has been by mutual agreement, from the moment I arrived until my departure today."
"I'm leaving by the front door."
MAJOR FORCE
Kaka, who scored in a 4-0 win in Uruguay on Saturday, is with Brazil's squad for the World Cup qualifier at home to Paraguay on Wednesday.
He said he was sure he could help his new club, overshadowed this season by treble-winning Barcelona, become a major force in Spanish and European football again.
"I'm sure Real Madrid will build a competitive team which can start winning titles again as they have always done throughout the club's history," he said.
"I'm sure Real can become major competitors in Spain and in European football."
Kaka brushed off a suggestion that he could wear the coveted number five shirt previously worn by Zidane and said the Frenchman would be an example to him.
"I don't know what number, I'll take my time choosing it and I'll respect the numbers," he said.
"I'm grateful for the five (suggestion), but I think Zidane is Zidane. To avoid any type of comparison, I'm going to try and write my own history. But Zidane will serve as an example to me."
He also had encouraging words for Milan's new coach Leonardo.
"Leonardo will have been a player, director and coach of the same club and I don't think many have achieved that.
"I hope I'm helping because there will be some money coming into the till. Leonardo has the ability to keep Milan on the right track."
More Kaka from FourFourTwo:
Kaka joins Madrid from Milan
Shy-boy demeanour hides ambition
Kaka leaves Milan as best friends
Kaka's exit a fresh blow for Italian football
Kaka: the factbox
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
