Pellegrini, celebrating his 23rd birthday on the day, crashed a late shot off the post - as the Azzurri suffered defeat against the run of play at Bologna's Dall'Ara stadium.
Nicolo Zaniolo was a late substitute in the match, although he could not help turn things around after Krystian Bielik's first-half strike.
Luigi Di Biagio's side face Belgium in their final group game, needing to win if they are to progress to the semi-finals of the competition.
The game takes place on Saturday at 21:00.
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