The Wales international, who was born in Cardiff, has been out since late April with a calf injury but returned for Real on Saturday.
He came on for Karim Benzema to play the final 18 minutes of the final, and was full of praise for his home city when talking to reporters after the match.
“We’ve made more history so we’re just very happy to win the 12th and we’ll enjoy this moment now,” Bale told BT Sport.
“We knew it was going to be a tight game – it was all about taking your chances and we did that. These are incredible scenes here. The city have done a great job in staging the final.
“On a personal note, to win at home is a dream come true.
“It’s been a hard season, I worked hard – at one point I thought I wasn’t going to make it to the final but I’ve worked tirelessly at home and this is the reward you get for all the hard work you put in.”
Cristiano Ronaldo broke the deadlock in 20 minutes in the final before Mario Mandzukic equalised for the Old Lady.
Casemiro restored his side’s lead after the break before Ronaldo created some breathing space just three minutes later.
Marco Asensio had the final say for Real, netting a fourth in stoppage time.