But Redknapp says the footballing culture in this country has to change if England are ever to challenge.
He told Sky Sports News: "We did okay. Roy (Hodgson) came in at a difficult time.
"We came out of the group which wasn't the most difficult group in my opinion and then didn't play very well against Italy.
"I don't think anyone expected a lot more but I still think we've got players in this country that are capable of doing a lot better and hopefully Roy will take them on now.
"He's got time to work with the team but I think it's long term.
"Unless someone sorts it out and we start playing and producing people that are technically better and are willing to play from the back and receive the ball and play like Italy played against us where they passed the ball - like the top teams in the world - they are never going to improve.
"The problem is they can set up Burton and have the kids there and work on their skills and on their technique. The problem is they then go to football clubs and it depends how the clubs play.
"If the clubs are not going to play it's no good having somebody who is going to be the new (Andrea) Pirlo and that kid goes to a club where they are lumping the ball from back to front 60 yards.
"Unless they are going to play through these people and they are going to encourage more and more teams to play football then we are always going to have that problem."