Real had led through Angel Di Maria's earlier strike at the Mestalla in Valencia on Tuesday night, but Barcelona levelled just after the hour through youngster Marc Bartra.
However, with the game looking set for extra-time, Bale produced a wonderful run and finish with just five minutes remaining.
"It was his most important goal, it was the most defining moment of the game," Ancelotti said in the post-match press conference.
Midfielder Xabi Alonso added: "The goal was incredible , I don't think I've seen anything like it. It looked like the ball was going out and he was under pressure, he ran off the pitch to keep it in, it was just amazing.
"Now we have the taste of victory. It was a really exciting game, with both sides playing at their best."
The win earned Ancelotti his first trophy since succeeding Jose Mourinho as the Madrid boss last summer, and kept the team's hopes of winning a treble alive.
Ancelotti added: "I think we played very well, we were playing against a very strong team. We had to suffer at times but I think it is a deserved victory. We are very proud to have won this competition.
"More than anything, I want to congratulate the players. The atmosphere inside the stadium from both sets of supporters was fantastic, I am happy to be here and to have experienced this spectacle."
Next up for Madrid is their Champions League semi-final tie with holders Bayern Munich, while they trail Primera Division leaders Atletico Madrid by three points with five games of the campaign to go.
Barca, meanwhile, look set for their first season without a trophy since 2008, knocked out of the Champions League by Atletico and four points adrift of Diego Simeone's side in the table.
However, Ancelotti refused to write off the Catalans.
"You cannot say Barcelona are finished, not everything has gone well for them this season but I think they will remain hopeful of achieving something until the end of the season," he said.
"We can say from experience this season that playing against Barcelona is very, very difficult. At times, you need a bit of luck to win. In my opinion Barca are not a team at the end of an era. They are still very dangerous."
Barca boss Gerardo Martino could not hide his disappointment at his side's third straight defeat.
"Obviously this is not a happy time for us," he said.
"It has been a very hard week for us but there is nothing else we can do but look ahead to what is left of the league season.
"It is a very hard blow to take, the expectation on us today was huge and it was a final so everyone was desperate to win."
However, the beleaguered coach vowed to keep going until the end of the campaign.
"I am hurting due to the defeat and for the people that came here with great expectations to support us, but we still have a lot left in the tank," he said.
"There is no recipe for recovery. The league doesn't look favourable for us but we are obliged to fight on until the last day."