Redknapp, who cited the "superb" backing of the Portsmouth crowd as one of his reasons for turning down a lucrative move to Newcastle two weeks ago, said: "Our supporters know what I think of them. They are tremendous and never let us down.
"We are going to do all we can to have an FA Cup run this year and also keep things going in the league. It would be fantastic for this club to go to Wembley and I would love to lead the team out there.
"But we've got to watch out we are not the latest victims of a shock result - as so many of the Premier clubs were in the last round.
"I'll be putting out a strong team to face Plymouth because I've been on the wrong end and the right end of cup upsets in the past and I know what is the better feeling."
Redknapp, who took most of his squad to Fontwell Park races yesterday, has skipper Sol Campbell (back) and midfielder Sean Davis (foot) back in training after injuries, with Davis playing a full 90 minutes for the reserves in a 1-0 defeat by West Ham on Wednesday night.
He said: "If Sol's fit he will certainly play and Sean should be in the FA Cup squad as well."