A 2-0 win at Liverpool on Sunday put them in pole position for the final Europa League place but that is little consolation after their exploits on their debut among Europe's elite earlier in the campaign.
"There are six teams (challenging) for that top four," said Redknapp. "Manchester United are certainties, Chelsea are certainties and you have to fancy Man City next year as they are going to spend another ?£100million."
He added: "You also have to fancy Arsenal, because they have been there every year, and Liverpool are a great club with great tradition and they will be back stronger with Kenny (Dalglish). We could have improved (the squad) in January. It wasn't a case of spending, we just needed a little tweak to liven us up a bit because we had a few tired players around.
"Hopefully we can get one or two players in the summer and improve again for next year because it is going to be hard. We have a big squad but what we need is one or two players who will make the difference to us.
"Liverpool have done that with Luis Suarez, he is going to be a big player, and we need to find one or two to keep us pushing for the top four."
While the priority will be looking for new arrivals, Redknapp knows he has some big decisions to make in terms of what happens with a number of his squad who have failed to come up to scratch this season.
None of this three strikers - Peter Crouch, Jermain Defoe or Roman Pavlyuchenko - have impressed while he has found things stretched at the back because of injuries.
Injury-prone centre-back Jonathan Woodgate appears destined to leave when his contract expires next month, having played just four times in the last two seasons. Ledley King's appearance at Liverpool was his first since mid-October and while he still has 12 months left on his current deal, a long-term knee problem regularly restricts his involvement.
"We have some players to shift now, we have players on loan who will be coming back and I'm looking for a good frontman if I can find one," added Redknapp. "I went to the cup final in France on Saturday night and I'm going to go abroad two or three times this week and keep following up leads and see what we come up with."
Source: PA
Source: PA