Spurs looked set to be humiliated when holders Inter raced to a 4-0 lead inside 35 minutes through goals from Javier Zanetti, a Samuel Eto'o penalty - after Heurelho Gomes had been sent off - Dejan Stankovic and Eto'o again.
But Bale almost completed a sensational comeback single-handedly, scoring one of the goals of the season before netting twice in the closing seconds to further enhance his burgeoning reputation.
The Wales international was coy about his achievement after the match, however, insisting the only thing that mattered was the team performance, which improved markedly after an awful start.
"It's hugely disappointing. We all knew we could do better in the first half. We started off sloppy and we paid the price," Bale told ITV1.
"But I think with 10 men we showed what a good team we are, and if we'd had 11 men on the field it could have been a different game.
"It just wasn't a lively start and we paid for it. I think next time we'll learn from this mistake and hope not to have a start like that ever again."
Asked what was going through his mind when he completed his hat-trick, Bale said: "I just had the ball and put it in the back of the net. There wasn't too much to think about.
"I was more thinking about getting back into the game, and we did that. But time ran out on us."
Bale and Spurs at least have the chance to put the ghosts of the San Siro to bed when they meet Inter in the return fixture in a fortnight.
"We had a lot of positives come out of the second half. We kept the ball well with only 10 men, and
hopefully at White Hart Lane we can do a better job and get a victory," he said.
"The result is what matters and it's massively disappointing. We want to put that right next time."
Spurs boss Harry Redknapp admitted he feared the worst after witnessing his side's nightmare opening to the match.
"We were bang in trouble at 4-0 down. Any kind of score could have come. We could have been sitting on the end of a seven, eight, nine-goal defeat with 10 men against Inter Milan," he told ITV1.
Redknapp admitted he did not think his players would run Inter as close as they did come the final whistle, saying: "I'd be a liar if I stood here and said I saw that coming, but second half we got at them at every opportunity.
"I left the two wingers on and we had a go. It was a fantastic hat-trick from Gareth Bale, an amazing performance again from him.
"He's as good a left-sided player as there is anywhere around, possibly there wouldn't be too many in the world better than him at the moment."
Asked what such a performance would do for Bale's value, Redknapp added: "He's not for sale. He's here and we're looking to build a club at Tottenham, not dismantle one."