Redknapp said: "It is a terrific performance away from home. We are on a great run, scoring goals away from home and looking very strong.
"Villa Park is not an easy place to come and to score three goals as well as missing other good opportunities was a tremendous performance.
"However, I would think that the top four are on another level to us. They have got the squads and are strong.
"These are great times for Portsmouth, however, 11 games unbeaten. We should make the most of these times."
Villa boss Martin O'Neill said: Even though we lost against Arsenal, I felt our confidence was enhanced if anything going into this game.
"But we get knocked back by a fluke of a goal by Craig Gardner and their other two goals are from wonder strikes.
"But we still had chances and had we taken them it would have been a different story. Martin Laursen had a great chance to make it 1-1 and David James produced a fantastic save to halt Gabriel Agbonlahor. That would have made it 2-1 and would have made a big difference in the game.
"We have a decent belief in the team and when we pulled one back late on through Gareth Barry's penalty, I still felt we could get something from game."