Speaking to the club's official site, Redknapp said: "It's going to be interesting playing in the UEFA Cup, but we need a big squad with the number of games it involves.
"It's difficult to maintain a strong league position and do well in Europe. To do that you need a big squad that you can rotate.
"I think we need four more good players for a squad capable of fighting on both fronts.
"I need a striker: I've only got Jermain Defoe, David Nugent and Kanu. I might even need two strikers, in all honesty, now that Milan Baros has gone back after coming here on loan.
"Milan did all alright for us. He's a good lad and worked hard. But I'm really looking for someone to play with Jermain Defoe."
Some fine-tuning of the £9million bid for him should see Crouch arrive at Fratton Park despite reported interest from Tottenham.
"I'd like another centre-half, a position where we desperately need cover," added Redknapp, although Richard Dunne is looking less and less likely and Younes Kaboul is now being courted by Juventus and Middlesbrough.
"I'd like another wide player too, because we're still short in that area even though we've signed Glen Little.
"And I may need someone who can play centre-half or midfield. I know the players I like, but getting them is another thing. It's a waiting game."