"I need a goalkeeper, someone fresh who can push Shaka Hislop," said the Pompey boss.
"I am also looking at another signing, a midfielder. He will probably be a free transfer but he'll be another good player. That is how I have always had to work, ever since I came into the game.
"Three of the players I signed were on a Bosman and the other cost £1.5million so I don't think we have done too badly."
On the Sheringham signing, Redknapp added: "Sometimes you have to gamble. I don't think Teddy is a gamble but obviously other people do because they haven't taken him.
"If he was 21 he wouldn't be coming here, but I think he has got so much to offer. He is a class act and he'll be massive around the place for us."