Ancelotti won his first piece of silverware with the club thanks to Gareth Bale's stunning 85th-minute winner.
Real broke the world transfer record to lure Bale to the Spanish capital in September and he repaid their faith by storming half the length of the pitch before ending his left-wing run with a composed finish.
It came after Marc Bartra's 68th-minute opener cancelled out Angel Di Maria's early goal, and continued Barcelona's week of misery.
"I'm very happy for winning the cup," Ancelotti said.
"We deserved to win. It was a difficult match because we played a tough rival … it was a great match.
"Bale scored an important goal at a critical moment. Everyone played well because they played as a team, compact as always.
"We gave away a few balls in the first half but the team worked hard and did well."
Ancelotti also singled out Isco for praise, before insisting that Barcelona's season was not over yet.
"I think Isco is doing well at the moment and is giving us a lot of quality," he said.
"I think Barcelona played well. Maybe things haven't worked out for them this season, but they will still fight for La Liga."
"It was a very nice game where we had chances (for) both teams, but we are just worthy of victory," Casillas told the club's website.
"It's time to remember Jese, who also deserves (this).
"(He) will soon be with us … (we're) very happy for the fans. Now we have to enjoy it and think about the league and the Champions League."
Alonso added: "It was awesome, we are very proud. This title tastes heavenly."
