The Italian champions fought back from a goal down to draw 1-1 at the Bernabeu to set up a Champions League final against Barcelona in Berlin on June 6 with a 3-2 aggregate win.
Bale, the world’s most expensive player, had another disappointing night in front of his own fans and missed a string of chances as Madrid crashed out of the competition.
Defeat saw Real miss out on a first El Clasico European decider and, while disappointed, Bale insisted he had been happy with his general performances during a campaign that has seen him come in for repeated scrutiny.
Speaking to Sky Sports, he said: “It was very disappointing, we wanted to be in the Champions League final to give ourselves a chance of winning but it was not to be and we will go again next year.
“We always try and score as many goals as we can but it wasn’t meant to be tonight. They (Juventus) played a good game and obviously we are disappointed but we will have to regroup and come again next year.”
Bale had Madrid’s first chance of the night, heading over after just 35 seconds, and at least two presentable chances in the second half but never once managed to test Gianluigi Buffon in the Juve goal.
“I was unlucky not to grab one,” he said. “As long as I keep trying, usually one goes in. Unfortunately it didn’t happen tonight and you move on.”
His best chance was a back-post header which he sent over from point-blank range.
“I got a slight touch (in the back) and I couldn’t get over the ball,” he said. “It’s one of those things that happen in football and you move on.”
The defeat all but ends Madrid’s season as they sit four points behind Barcelona with two games left in the league.
He said: “It’s obviously disappointing and not what we want but as I said there is still a chance to win the league and we will keep fighting until it is mathematically impossible and that is all we can do.
“There have been some ups and downs (this season) but I feel personally I have played well but not scored as many chances, important chances, as I like but my general play has been good. I think my finishing has been a bit rusty this year and that’s something to work on for next year.
“What doesn’t kill you makes you stronger, and I’ll learn from this season a lot and take it into next season and have a good season.”