England were beaten by Italy at the quarter-final stage in a game which starkly displayed their deficiencies, specifically an inability to retain possession and inferior technical ability.
For Redknapp 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."
Redknapp, Betfair's football ambassador for Euro 2012, also expressed surprise that David Beckham has not been selected for the Great Britain team for the Olympics.
"I have to say that I would have picked him," he said.
"David has been a fantastic servant to all his clubs and a tremendous ambassador for football.
"He trained with Tottenham in January 2011 and we looked at signing him on loan when the American season ended. Putting him in the Olympics squad would not have hurt.
"Fair play to Stuart. He's always been his own man, which is what you have to be if you want to make it as a top manager. It's up to him to select the best squad at his disposal, that's what he believes he'll do."
Redknapp, meanwhile, has revealed he tried to sign Balotelli while he was Tottenham manager.
Balotelli guided Italy into the final of Euro 2012 on Thursday by scoring both goals in the 2-1 victory over Germany.
The 21-year-old is a volatile character and had a turbulent season although he ultimately secured a Premier League winners' medal with Manchester City.
Redknapp said: "You never know what you're going to get with Mario Balotelli but one thing is certain - he is a major talent.
"He stunned Germany in the Euro 2012 semi-final and his second goal was fantastic.
"I actually tried to sign him for Tottenham before he went to Manchester City. I'd admired him for a while and I went over to Italy to watch him play. I was impressed and I met up with him too.
"We wanted him on a loan deal but his club weren't keen and it never happened. Shame because he's definitely got it and, at only 21-years-old, he'll be terrorising defenders for many seasons to come."
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