They lost 2-1 to hosts France in their last-16 clash in Lyon.
Robbie Brady converted a penalty in the second minute after Shane Long was brought down by Paul Pogba to give them a 1-0 lead.
Antoine Griezmann headed in the equaliser for France after 58 minutes before he added a second to make it 2-1 three minutes later.
Ireland were reduced to ten men when Shane Duffy was sent off after 66 minutes.
Griezmann was through on goal when Duffy took him down outside the box.
