The Welshman was over the moon with his winning goal against Barcelona and is desperate for more silverware this season
The Wales international helped Madrid to their 19th Copa del Rey win in history with a superb solo goal after Angel Di Maria and Marc Bartra had previously found the net in Valencia.
Bale - who surged past Bartra before poking past Jose Pinto with just minutes remaining - says the Barcelona defender could only try to push him in vain as he secured Carlo Ancelotti's first triumph as Madrid coach.
"I had to sprint, Bartra pushed me and tried to block my path but wasn't able to. I had to go around him," Bale told the official Madrid website.
"It was great to score the goal but even better to win the match and pick up a title for Real Madrid. I'm delighted to have won my first title with Madrid. I think we could go on to win even more this season.
"The atmosphere was fantastic. It has been a perfect night.
"This win is for all the fans and we hope that it will be the first of many to come. We have worked hard as a team."
Real Madrid resume La Liga action on Saturday with an away game against Valladolid.