The Azzurri were losing 2-1 in the penalty shoot-out after Riccardo Montolivo had missed his attempt when Pirlo chipped the ball straight into the middle of the net as England goalkeeper Joe Hart dived to his right.
Ashley Young and Ashley Cole then missed from the spot, allowing Italy to win 4-2 in the shoot-out, and Pirlo hinted that his penalty changed the game.
"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.
"England did not create any chances during the match. 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."
Pirlo's Juventus team-mate Gianluigi Buffon also commented on the nerve-wracking quarter-final, and admitted that despite Italy's dominance, he was dreading an England victory from 12 yards.
"It is clear that I feared an upset, in the penalty shoot-out you can be lucky and win or unlucky and lose. With regards to the 120 minutes of action, we deserved the victory, we created more chances than them," the goalkeeper pointed out.
"After Montolivo missed his penalty, I only thought that I should save as many as possible, because my team-mates deserved to win the match, and so did I."
For Daniele De Rossi, who was forced off through injury, Pirlo's shoot-out heroics were the highlight of a tense match on Sunday evening.
"Pirlo's penalty? It has been many years since I saw one this beautiful. It reminded me of Totti's penalty against Netherlands in 2000," he said.
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"Justice was done, we played better than England. We controlled the match from the first minute," he claimed, adding that the only thing running through his mind in the shoot-out was marking a goal with his goalkeeper.
"I did not think anything while I was taking my penalty, I only thought about scoring and go to Buffon and celebrate with him."
Italy will now take on Germany in their semi-final clash, which will be played on Thursday in Warsaw. Pirlo had the last word as he asserted that, from this point forward, anything was possible.
"At this stage of the tournament we should not rule anything out, that is the reason we are here," he added.