Spurs lead 2-0 at Old Trafford on Saturday before the champions hit back in the second half - starting with a controversial penalty award - to win 5-2.
Midfielder Jermaine Jenas feels they can still claim seventh and a place in the Europa League, but Redknapp has instead targetted a top four finish next time out.
Off to a flyer: Luka Modric scores for Tottenham at Old Trafford, but his side were eventually defeated
'I'd like to think that we will be pushing the top four, with Aston Villa and Everton, next year,' the former Portsmouth boss told London's Evening Standard.
'It's about time somebody broke into it. We just need one or two players in to improve us and if I get those in, then we will be strong next year.'
Tottenham seem to be perenially linked with deposing Manchester United, Arsenal, Chelsea or Liverpool but have failed to better fifth in the Premier League era.
Jenas lays into ref for United debacle but insists Spurs can still claim Euro spotMan Utd 5 Spurs 2: The moment that Webb handed the title to UnitedHATCHET MAN: Harry must scrap Cisse swoop as Tottenham boss draws up his summer hitlistCompetition: Win VIP tickets for Spurs v West Brom at White Hart Lane on May 2TOTTENHAM HOTSPUR FC