The Italian, who had signed a three-year deal, told president Florentino Perez as much.
'La Decima' had turned into somewhat of a curse for the La Liga giants, who were without an appearance in the UEFA Champions League final since 2002.
But that changed in Lisbon on Saturday as a 4-1 win over city rivals Atletico Madrid saw Real to a record 10th title.
Plenty of credit must go to Ancelotti, who has brought stability and led them to a double in his first season in charge.
"On my first day, when I went to the Santiago Bernabeu trophy room, I said to the president that there was one cup missing and that we should try to get it this season," Ancelotti said after Saturday's win.
"We've managed to do that.
"I've felt a lot of trust in me from the whole of the club, and we've had the composure to win games."
Real did it the hard way as Diego Godin opened the scoring for Atletico, capitalising on goalkeeper Iker Casillas getting caught in no-man's land.
Ancelotti's men needed until the 93rd minute to level as Sergio Ramos headed in a Luke Modric corner to force extra-time.
"What was most difficult was to get the equaliser," Ancelotti said.
"We didn't have any space, Atletico defended very well, but we tried every way possible, right to the end – we managed to do it and then the game changed completely.
"The goal we scored gave us a lot of strength and after that perhaps we wanted the victory more."
Angel Di Maria's dazzling run and strike, well saved by Thibaut Courtois, led to Gareth Bale putting Real ahead in extra-time.
Marcelo and Cristiano Ronaldo, never to be denied, added the polish against the tired-looking La Liga champions.
"I am lucky, but not for this game," Ancelotti said.
"You can say I'm a lucky man in the end, or you can say that we tried to do everything until the last second of the game.
"This is football – sometimes you have bad luck, sometimes good luck."
