Pirlo, 33, was named as UEFA's official man of the match after controlling the tempo of the game during a goalless 120 minutes and then scoring an audacious chipped spot-kick as Italy won 4-2 on penalties.
It was no less than Italy deserved after a superior performance, though they had to come from behind in the shoot-out after Riccardo Montolivo missed their second penalty.
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."
On the game as a whole, he added: "I wasn't surprised by tonight. I knew we could control the game.
"My worry was that we were allowing England too much space on the break - we could have been a bit cleverer in our build-up play.
"We tried to play football. We tried to draw England out, we tried to hit them quickly. I think if we'd scored in the 90 minutes it would have been an even better game."
Montolivo, who will depart Fiorentina for AC Milan when his contract expires this summer, was grateful to keeper Gianluigi Buffon, who saved Ashley Cole's penalty after Ashley Young had hit the crossbar.
The 27-year-old said: "It was a great relief, especially for me. I felt terrible after missing my penalty, it was really a tough moment but fortunately it ended well - we are lucky to have a goalkeeper like Buffon."