First-half goals from Samir Nasri and Marouane Chamakh had put Arsenal in complete control, but Gareth Bale's slick finish reduced the deficit before Rafael van der Vaart scored a penalty and Younes Kaboul headed in a late winner.
"To come back showed great character, it really was a fantastic second- half performance," added Redknapp after Spurs' away win at a so-called "Big Four" side for the first time in 69 games.
"I gave them a rollicking at half-time, and woke them up a bit. We took the game to them from the start of the second half. We had to go for broke. It wasn't a case of trying to stem the tide, it was a case of trying to get back into the game.
"We were either going to get beat 5-0, or have a go. That's what we did, because that's my nature."
Arsenal manager Arsene Wenger admitted that to have lost three matches at home already this season was not the form of potential champions.
Defeat by Spurs 'painful' for Wenger
"It's difficult to understand how we lost the game, because of the number of chances we created compared to Tottenham," he said. "I'm a bit speechless.
"But we lost our focus, and we were punished. We made some basic mistakes.
"It's a shame because overall we had a good game, after recent weeks. But we were not rewarded. We did not keep our concentration for 90 minutes and, when you want to win, that cannot happen. We eased off a bit, that is for sure."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.