The Juventus star was the player of the match, but was unable to inspire the men in blue to a victory over 120 minutes.
But with the Azzurri losing 2-1 in the shootout after both sides had taken two penalties, his imaginative spot kick swung the momentum.
The chipped penalty, made famous by Antonin Panenka in 1976 when he scored to win Czechoslovakia the European Championship in a shootout, looked risky, but Pirlo claimed afterwards that his choice was a calculated one.
"Joe Hart was doing some strange movements, so when he dived I decided to take it like that and it went well," the Juventus midfielder told Rai Sport.
"It put a bit of pressure on their takers and in fact Ashley Young missed his penalty after that.”
Italy now play Germany in the semi-finals, and Pirlo said he felt justice had been served by Italy’s victory.
"England did not create any chances during the match,” the Italian added. “They played for the penalty shoot-out, while we wanted to win.
"We knew we could dominate the match, and all that England did was defend. We used up more energy than we expected, but we were able to win the match."
His manager Cesare Prandelli paid tribute to the midfielder's composure and class after the match.
Prandelli said: "When Montolivo missed his penalty I was sad as he was one of the best players tonight. When Andrea Pirlo stepped up I was very calm - he's a star and knew what he needed to do; and he did it."
He added: "Penalties are a lottery but I thought we deserved victory in the end. I was watching with my arm around my son and I told him he was lucky he didn't have to buy a ticket.
"Around 80% of penalty shoot-outs go down to luck. Some players are used to this kind of pressure, some are just calm in these situations - but mainly it's down to good fortune."