Newcastle kept Tottenham's attack at bay before Aaron Lennon opened the scoring shortly after the break and Bale added a second late on - his 10th of the campaign - with a fine finish from a typical surging run.
"The first half was scrappy and went the way Newcastle wanted - they filled up the midfield. We got round the back of them twice and that's how the goals came," Redknapp continued.
"Aaron has to continue to drive outside and drive inside, that's what he did today. Gareth's done that all season. He went on the outside of Newcastle defender Steven Taylor and smashed it in.
"Ten goals is an amazing stat for Gareth. You want your central midfield player to get six or seven and your front men to get a few more, but he's scored his goals as a winger."
Redknapp had no sympathy for Kaboul, who was sent off midway through the second half for appearing to thrust his forehead at Newcastle's Cheik Tiote.
"If he's put his head in his face he had to go off," Redknapp commented.
"He showed a lack of discipline. Other people will now come into the team while he's suspended, and they'll make it difficult to be shifted."
Meanwhile, Newcastle manager Alan Pardew was left to rue his side's lacklustre attacking display at White Hart Lane.
"I thought a lot of things we did today were very good, we nullified Spurs to a certain degree," Pardew reflected.
Pardew blames 'attacking quality'
"We had opportunities to hurt Spurs, but we were poor and not at our best.
"Their first goal had an element of fortune because our keeper Tim Krul could have saved the shot if it hadn't taken a deflection."
One player who pulled out of the squad after picking up an injury was left-back Jose Enrique.
However, Pardew was fuming after learning that the Spanish defender had revealed his fate on Twitter.
"Did he tweet it, did he?" Pardew asked reporters after the defeat.
"Players can't be giving that sort of information out. It's difficult to police - we need to make it a club policy that it has to stop."
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