Bale was started on the bench by Zinedine Zidane for the title decider against Liverpool in May but proved to be the difference between the two sides after being introduced around the hour-mark.
The Wales international needed just three minutes to have an impact, his stunning overhead kick giving Madrid the lead before he sealed a 3-1 win with a long-range strike late on.
Bale admitted starting on the bench had angered him, and his feelings were unchanged when he was introduced.
"Angry. Quite angry, to be honest," he told the Daily Mail.
"Obviously, I felt I deserved to start the game. I'd been scoring goals. So yeah, I suppose it was hard to put the anger aside."
Bale had an instant impact once introduced, meeting a Marcelo cross with an incredible overhead kick that flew into the top corner.
The 29-year-old said he knew immediately his strike was a good one, after admitting the unorthodox move was instinctive.
"You could opt to take the ball down and do something then. But you know you are in a situation where if you're going to get closed down you have to try something," Bale said.
"You certainly don't really think about looking stupid. If you don't try things, things never happen. If you have time to think about it, it doesn't come off. It's when you have to make those reaction decisions that you normally tend to get the best result.
"I knew exactly where the ball went and you can see in the video my head turns to look exactly where the ball is going. As soon as I hit it I knew it was good."
Bale has made a fine start to the new season, scoring three goals in four games for Madrid in La Liga as last season's runners-up have won 10 points out of a possible 12.