Despite an impressive start to the campaign, with Spurs winning their opening four league games, defeats to United (3-1), Chelsea (3-0) and Arsenal (3-0) have highlighted that the White Hart Lane outfit are still some way short of becoming genuine contenders for a top-four spot.
Having contained the Gunners for the first 41 minutes at the Emirates Stadium last weekend, the visitors' hard work was undone in a mad two-minute spell, with goals from Robin van Persie and Cesc Fabregas effectively ending the contest.
But despite being comfortably beaten by their arch rivals, Spurs' supremo Redknapp still believes Arsene Wenger's side will lag behind the experienced squads possessed by current top-two Chelsea and United.
"I think Arsenal are potential winners but personally I don't think they will win it, that's only my opinion," he said in The Independent.
"I'm not writing them off, they've got a good chance. But I think the winners will come from Chelsea or Manchester United.
"I don't think it's a soft centre [at Arsenal], I think it's maybe a little bit of a lack of experience still. They're not an experienced team, it's still a young team, a fantastic young team.
"But I just feel Chelsea and United, they have players who have been there and done it all and been the full course in the championship race."
