"I only wish Portsmouth every success," said Redknapp.
"I took a team when they were bottom of the league and we had no players but we built a squad there, a fantastic group of players.
"I thought I left Portsmouth in the best possible shape - they are a fantastic bunch of players and whoever gets the job will carry it on. It's a bigger club than me, that's for sure.
"It wasn't a money move - lots of people said after the FA Cup win that I should leave then.
"I have done as well as I can on the resources - the support is great and they love their club but I've done my job there.
"I've kept them up and won the cup...but this is a chance to take on another big challenge."
He added on BBC Radio Five Live: "It's time to move on - lose a few games and people start wanting you out.
"The fans have got so much to look forward to. They've got AC Milan coming up in the UEFA Cup - who would have thought they'd be coming to Fratton Park?"