Sunday’s 3-1 defeat at White Hart Lane left Spurs only four points ahead of fourth-placed Arsenal, having previously held a ten-point lead over their rivals and Chelsea.
Redknapp's side now face stiff competition for third, which guarantees entry into the lucrative Champions League group stage, with two difficult away games approaching at Everton and Chelsea.
However, the former Portsmouth boss appeared undaunted, telling reporters: “We're still in pole position. I still fancy us to finish third.
"That 10-point lead has suddenly become four points and we've got some hard games to come. We go to Everton and we've got Chelsea away.
"It's going to be tight but I'd still rather be where we are than Arsenal. We're four points in front and we've still got a big chance.
"I'm looking to finish third, not fourth. I'd be disappointed if we finished fourth. I'd be even more disappointed if we finished fifth!"
Defeat to the Red Devils came despite a strong Spurs performance in the absence of key players Scott Parker, Gareth Bale and Rafael van der Vaart.
And Redknapp believes there are plenty of positives to take from the match, if not the result.
He added: "We played so well first half and to come in 1-0 down, it was unbelievable, really. We dominated the game, did absolutely everything I asked them to do.
"All over the park, I felt we dominated the game. Then we start the second half in exactly the same fashion.
"We get on top again and then we don't pick up from a throw-in and we find ourselves two down when they've done nothing.
"They were there to be beaten. I've not seen Alex on his feet as much for years, it wasn't going their way, but that's how it goes sometimes in football."
The 64-year-old was also adamant that speculation regarding his potential appointment as the next England manager had not affected his club.
When asked if he had been distracted recently, he replied: "No, not at all.
"We trained on Saturday morning and then I went to watch QPR play Everton because we play Everton next week.
"My focus is completely on getting result here and the players know that. I don’t have days off. I am here every day – my only focus is on Tottenham. It has had no effect.
"You can’t say the players haven’t tried today. They have worked hard against one of the best two teams in the country. I could not fault the effort."
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