Aaron Lennon and Benoit Assou-Ekotto were both on target as Spurs coasted to a 2-0 victory over Everton to move within three points of Barclays Premier League leaders Manchester City.
The Spurs boss said: "The pressure is on Man City because you look at their squad and you look at the money they have spent on the likes of Sergio Aguero, Edin Dzeko and Samir Nasri. With the money they've spent on wages and transfers, they are expected to be there and win the championship."
He added: "They and Manchester United are red-hot favourites I think, but we are just hanging in there at the moment. We are playing well. We are right there."
Redknapp's men are now level on points with second-place Manchester United and will go joint top with Manchester City if they beat Wolves on Saturday.
Tottenham were huge outsiders for the title in August, when they began the season with heavy defeats to the Manchester sides, but they are now viewed as serious contenders to win their first championship in 51 years.
Redknapp thinks his team are capable of pulling off an unexpected win and also believes that his team will have the added bonus of playing through the rest of the campaign without being under the same pressure as City and United.
He said: "It's not impossible for us to win the league. It's difficult, but not impossible. We are a good side. We have some real quality.
"We are playing well, playing with smiles on our faces.
"We are not going out there under severe pressure, trying to nick a point to stay in the league."
Source: PA
Source: PA