The former Tottenham manager feels that the Arsenal youngster is capable of delivering the midfield stability that his country are in need of in future competitions
The Three Lions were chasing shadows for long periods in the Kiev tie, and although they managed to hold the Azzurri for 120 minutes, they eventually lost on penalties.
And Redknapp, who was widely linked with the England job before Roy Hodgson was eventually appointed in April, feels that his compatriots must learn to retain possession more effectively if they are to progress.
"The difference in the two teams shows that if you are going to compete on the world stage you have to be able to keep the ball," he explained to The Sun.
"Look at Pirlo against England — he had no pace, strength and he’s ancient. But what a fabulous display. We must learn a lesson from this and do our utmost to produce an Pirlo of our own.
"He’s the type of player I’m talking about who doesn't rely on strength or speed — he’s a genuine footballer.
"It was the absence of Jack Wilshere which was felt most keenly. He can be our Pirlo. The only other midfielder we had in reserve was young Jordan Henderson.
"England struggled with that. But it is something Roy will definitely work on. He knows that it’s all about the future now and moulding the team his way rather than getting one together that is difficult to beat."
Despite the eventual loss to Cesare Prandelli's side, Redknapp feels that Hodgson can be proud of the job he did in Ukraine and Poland, with many England players performing admirably.
"Hodgson got the best out of the squad he had available to him in the time he had after getting the job," he continued.
"We played as positively as we could. England’s tactics were to react well and hit Italy on the counterattack.
"It was 4-4-2 or 4-4-1-1 with Wayne Rooney dropping in when he could. In the second half it was about hanging on and trying to use Andy Carroll’s power and height.
"Glen Johnson performed miracles in my opinion. He made last-ditch saves, superbly-timed blocks and looked good going forward.
"Gerrard was still our best player at Euro 2012. John Terry was magnificent.
"Let’s be fair to ourselves and the Italians and admit it’d have been an injustice had we won. They were by far the better team.
"I was pleased we came in level at half time. Italy dominated possession. They had twice as many touches as we did.
"It was hard for our midfielders to make much impact because they were overrun by Italy’s three in the middle. And they just got stronger and stronger as the game went on.
"They enjoyed that because of the extra man in midfield - Andrea Pirlo. It was hard for Scott Parker and Gerrard to get near him because he had two others who could peel off and get into space of their own.”