Three consecutive league defeats, against Arsenal, Manchester United and Everton, ended all talk of a first Spurs title since 1961. With Arsenal just a point behind in fourth place with 10 games left, Redknapp has re-adjusted his sights.
"If we finish in the top four I think we overpunched our weight really to be perfectly truthful with you but I think we will finish in the top four," Redknapp told reporters on Friday as he prepared his side for Saturday's visit of Bolton Wanderers in the quarter-finals of the FA Cup.
Tottenham could have gone 13 points clear of Arsenal when they led their north London rivals 2-0 at Emirates Stadium last month but ended up losing 5-2 and the Gunners have roared up behind them since after hitting form.
Chelsea are also four points behind in fifth place, meaning the final months of the season could be nerve-jangling.
At least on Saturday Tottenham can forget about the battle for Champions League football and concentrate on trying to reach their first FA Cup final since they beat Nottingham Forest in 1991.
"The priority is to get to the cup final and to get to a Champions League place," Redknapp, still favourite to be England manager, said of the goals for the remainder of the campaign.
"That's where we are at really - we want to go to Wembley if we can this year, certainly."
Tottenham will be without Aaron Lennon for the clash against relegation-threatened Bolton, while striker Emmanuel Adebayor is also suffering with a hamstring strain.
A year after taking Tottenham to the quarter-finals of the Champions League only to be hammered 5-0 on aggregate by Real Madrid, Redknapp said Madrid and holders Barcelona would be hard to stop again this year.
He was though impressed by Chelsea's dramatic victory over Napoli in the last 16 on Wednesday.
"Barcelona and Real Madrid I really think they are in a different level at the moment to anybody else in Europe," Redknapp said after the quarter-final draw raised the prospect of an all-Spanish final in Munich.
"So, if they have got through you would not see anybody beating Barcelona or possibly beating Real Madrid this year.
"I went to Chelsea the other night, it was a fantastic game, great performance, great game, it was a pleasure to be there and watch the game. They are still in there and I wish them well but they are going to have to go some, anybody would have to go some to beat the Spanish teams, that is for sure."
Chelsea, whose vacant permanent manager's job does not interest Redknapp, face Benfica with the prospect of Barca in the semi-finals if the Catalans beat AC Milan.
Real were drawn with APOEL Nicosia in the last eight.
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