The match ended 0-0 after 120 minutes of play. The Italians twice hit the post, and were thwarted by some poor play in front of the goal. Diamanti clipped the post with a curling cross in the 101st minute, and swept an open shot wide in the best chance of the second period of extra time.
Nocerino, another substitute, thought he had scored from Diamanti's cross in the 115th but was offside.
For England, it was yet another exit from a major tournament in the quarterfinals after a penalty shootout. England lost to Portugal in the same manner at Euro 2004 and the 2006 World Cup.
The first scoreless match at Euro 2012 was neither dull nor lacking good play. Italy had 35 shots, compared to only nine for England.
England had briefly led the shootout after Riccardo Montolivo missed Italy's second penalty. His shot went wide of Joe Hart's right post as the England goalkeeper guessed correctly.
Rooney then sent Buffon the wrong way, firing in his spot kick to the keeper's right to give England a 2-1 lead.
The momentum shifted after Pirlo tied it at 2.
Portland tops Seattle
Kris Boyd scored his fifth goal of the season, David Horst converted a header, and the Timbers (4-6-4) beat the visiting Sounders (7-5-4), 2-1. Seattle is winless in seven games, the longest streak in its four-year MLS history.
Red Bulls beat United
Defender Brandon Barklage scored the first two goals of his career and led New York to a 3-2 win over D.C. United before a franchise-record crowd of 25,187 in Harrison, N.J. The teams now are tied for first place in the Eastern Conference.