Aaron Lennon and Benoit Assou-Ekotto struck to secure a victory that moves Spurs within three points of Roberto Mancini's side, and leaves them trailing second-place Manchester United only on goal difference.
"I think the pressure's on Man City," Redknapp told reporters after the match. "You look at the money they've been able to spend - they’re going to be expected to be there [at the top of the table], certainly them or Man United.
"We're just hanging in there. Finishing above Arsenal would be a great achievement."
Redknapp admitted his players were beginning to believe Spurs have the capability to go all the way this season.
"William Gallas came in the other day and said: 'We’ve got a chance here,'" Redknapp said. "It's not beyond the realms of possibility. We've got some real quality, haven't we?
"We're playing with a smile on our faces. I've been saying all along it’s not impossible to win the title but it's very, very hard. But we're in there, we've got a chance."
The 64-year-old went on to hail his team's style of play and reserved extra praise for star winger Gareth Bale.
"What an athlete," said Redknapp of Bale. "If you don't enjoy the way we play, then you shouldn't be watching football.
"We gave most of the players a weekend off [for the FA Cup match against Cheltenham] and made changes and they were ready to go again."
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