However, Redknapp refused to raise his expectations for the rest of the season despite seeing late goals from Benjani Mwaruwari and Glen Johnson consolidate fifth place with a 2-0 win at the JJB Stadium.
Redknapp said: "We're a stronger outfit and we're getting better all the time. We played the big four in our first six games and now we've got 18 points which is a great start for us.
"That is a difficult group so if we can finish in the top half I'd be delighted."
The manner of Pompey's win was far removed from their 11-goal thriller against Reading last month but Redknapp admitted his side's dogged determination had given him plenty of satisfaction.
Redknapp added: "I said at half-time that the game was there for us to win. In games like that it is important we pick up points and I would not have been happy coming here and getting a point.
"We wouldn't have won these sorts of games six years ago because the players were useless.
"That's why I'm here and we've got stronger players now and we are a stronger outfit."