Redknapp's return to his former club resulted in a 2-1 win for Spurs although they did have Jermaine Defoe sent-off on the hour mark for violent conduct.
"I think that people hyped this up and with disrespect to Portsmouth fans, the way they were talking about how they would behave, I thought they were absolutely fantastic," Redknapp said after the match.
"You couldn't ask for better support than they gave their team and they enjoyed the game, I thought they were fantastic.
"They had a real go. That's typical Pompey spirit - that's how they are and how their fans are, they get behind their team, they will them on and we hung on for grim life in those last 20 minutes or so.
"We had a couple of breaks where we could have nicked a goal and killed the game - Aaron Lennon went through and he should have scored - but it was tough.
"Big Crouchy was up there on his own and we were getting pressed back deeper and deeper and in the end it was back to the walls stuff."
On the Defoe sending-off Redknapp fumed: "I was very disappointed with Jermain Defoe, getting sent off and reacting like he did..
"I said it was a day for cool heads, don't react if you get fouled, just get on with the game.
"Don't start kicking people or over-reacting and I repeated that to him at half-time on four or five occasions and he did react and he disappointed himself and I was disappointed with that as well.
"If he kicked him it's a red card and you can't do that."