In an eventful game in Tilburg, Germany drew first blood in the 19th minute when Josephine Henning headed home after Italian keeper Laura Giuliani spilled the ball following Dzsenifer Marozsan's free-kick.
Italy equalised from a counter-attack 10 minutes later as Ilaria Mauro nutmegged German keeper Almuth Schult after a pass from Barbara Bonansea who had sprinted down the whole length of the left wing.
Peter scored from the spot on 67 minutes after Giuliani had brought down Anja Mittag in the box, and a minute later Italy were reduced to 10 players as defender Elisa Bartoli picked up a second yellow card.
Germany hit the post twice — Sara Daebritz in the first half and Mandy Islacker in the second — while Bonansea saw her free-kick cleared by a diving Schult with 10 minutes to go as Italy were eliminated.
“I think this was a great Italy,” said Italy coach Antonio Cabrini. “We played on a par with a much better team than us. We had a great 70 minutes and believed in it to the very end.”
In the other Group B game, captain Lotta Schelin and Stina Blackstenius powered Sweden to a 2-0 win over Russia.