The Welsh winger, who moved to the club from Tottenham Hotspur for a record-breaking fee last summer, scored the winner as Madrid beat Barcelona 2-1 in the final of the Copa del Rey, and he was eager to pay tribute to his side's supporters.
"It was a perfect night," Bale told reporters. "It is great to win trophies and I am very happy to have won my first title with Real Madrid.
"This victory was for the fans for all the support they have given us, the atmosphere was fantastic."
Madrid can complete a treble this season, with Carlo Ancelotti's side still in contention to win La Liga and the Champions League.