Cork City manager John Caufield admits they were simply beaten by the better side.
The Leesiders lost 1-0 to AEK Larnaca in Cyprus last night and exit the competition after a 2-0 aggregate defeat over two legs of the second round of Europa League qualifying.
"You have to acknowledge that AEK are a very good side," Caulfield told RTÉ.
"You look at the heat, you look at the humidity, it’s hard to imagine when you watch at home on TV.
"There’s no shame in getting beaten by a side that are better than you and over the two games AEK were better.
"Our disappointment is that on both occasion we gave away disappointing goals."
Shamrock Rovers' European adventure ended in the Czech Republic last night.
Trailing 3-2 from the first leg, a goal from Jan Chramosta on 9 minutes killed the tie.
Golgol Mebrahtu added a second just after the half-hour.
Rovers exit after the Europa League after a 5-2 aggregate loss to Mlada Boleslav.