A beaming Bale said he would never forget the match.
"It was great. It was special beating the European champions. It will be a night that will never be forgotten," he enthused.
Once again, Bale tormented the right side of Inter's defence, prompting Spurs fans to chant: "Taxi for Maicon".
"A few of the lads were on about it after the match," added the Wales international.
"The supporters were unbelievable. They acted as a 12th man.
"They have been fantastic all season and we capped it off for them tonight. It was a special night."
Despite his new-found status as one of the most feared players in football, Bale was modest about his form.
"I'm just trying to keep my feet on the ground, work hard in training and do well in games and enjoy my football," he stressed. "I'm happy at the moment."
And Bale revealed that confidence throughout the team had improved after his hat-trick at the San Siro.
"We all had the belief that we could hurt Inter and we showed that," he said.
"We were unlucky to go down to 10 in the San Siro. With 11 men on the pitch, we know what we can do.
"We know what we are capable of. We just have to produce it and we have.
"Hopefully, we will have shown people what we can do and hopefully we can go far in this competition now.
Gareth Bale 'delighted' with influential performance
"We are just going to take it one step at a time and not get carried away."
The Italian media were also caught up in Bale's performance, with several major newspapers giving the Welshman a glowing report.
Turin sports newspaper Tuttosport put Bale's photograph on its front page under the headline 'Frightening Bale, he sweeps away Inter'.
While national newspaper La Repubblica announced: 'Nightmare Bale, Inter crashes in the home of Tottenham'.
Victory in their penultimate group game against Werder Bremen should be enough to seal Tottenham's progress and would arguably make them favourites to top the group as well.
"We are going to carry on working hard and go as far as we can," added Bale. "The most important thing is to get through.
"If we win the group, it will be a major bonus for us but we just want to keep working hard and get through to the knockout stages."
Crouch got on the scoresheet when he converted Bale's low centre, doubling Tottenham's lead after Rafael van der Vaart's opener.
Samuel Eto'o pulled a goal back for the reigning European champions but Bale rounded off his extraordinary evening when he scorched the Inter defence again to set up Roman Pavlyuchenko to score his side's third.
While Redknapp was understandably thrilled with Bale he was also eager to heap praise on the rest of his players.
He stated: "He was brilliant but the whole team was brilliant, from [goalkeeper] Carlo Cudicini, every one of them.
"There wasn't one of them tonight who didn't work and do exactly what we asked of them.
"It was an outstanding performance tonight, one of the great nights, I would think, at White Hart Lane that the fans have seen.
"It was a fantastic night. From the first to the last we played unbelievably. Pressed them, outworked them, outplayed them all night."
Tottenham now have seven points from their four matches and look on course to reach the knockout stages of the competition.
Given that Spurs complete their group fixtures with the home match against Werder Bremen and a trip to FC Twente - a side they thrashed 4-1 at home - Redknapp may have every right to be confident.
"We're in a good position now," he agreed. "It was a big game, playing Inter Milan at White Hart Lane, and everyone was here. All the Spurs fans can look back on it and I'm pleased to be part of that tonight.
"You have to put in perspective who we're playing against: Inter Milan, the Champions League holders.
"The opposition is top, top class and for us to play like we did tonight against them was a fantastic performance."
For Inter boss Rafael Benitez it was a disappointing return to England - and continued a run in which the former Liverpool manager has lost on his last four visits to White Hart Lane.
"When we scored I thought we were close," he said. "The team was growing and doing better. We were on top of them at this moment but the third goal changed everything."
Asked if Bale would get into the Inter team, Benitez said: "If he plays like today, why not?"
Bale is just amazing, amazing
Harry Redknapp reveals what Inter director Luis Figo said to him
Yet, as in the San Siro a fortnight ago, the former Liverpool boss once again felt his side gave Tottenham's rising star too much room.
"I think he was doing well away in the first game and he was doing well today when he had the space," said Benitez.
"We knew that if he has the space, it is difficult to stop him because he has pace."
Asked about Bale once again making life difficult for Maicon, Benitez replied: "Maicon is a very good offensive defender.
"He has more problem when players play like Bale, so we had to help him."
Redknapp revealed Inter director Luis Figo, the former Portugal midfielder, approached him after the match.
"He said to me, 'Bale is just amazing, amazing'," Redknapp revealed.
"When Figo says that, it's got to be good because he was such a fantastic footballer.
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