Robbie Keane and Tom Huddlestone struck the goals for Spurs in their 2-0 win.
Redknapp said: "Man City will be right there, Aston Villa will be right there and looking to push the top four. I think ourselves, the top four are very, very strong obviously and I think ourselves Villa and City will all be having a go.
"There's no reason you can't do it. It's not impossible to do. No-one has said you can't finish in the top four. You have days against Stoke when you murder them and days when you win 2-0."
Spurs were jeered off by their own supporters at half-time, despite leading, and Redknapp admitted his side were not at their best and had to rely on the heroics of Heurelho Gomes, who pulled off a string of saves.
"We were very fortunate, the keeper's had a fantastic day but that's how it goes," Redknapp added. "We got three points, you can play well and get nothing. We've got (Aaron) Lennon and (Luka) Modric to come back and when they come back we'll play differently again."