Goals from Ahmet Ilhan Ozek and Osman Tarik Camdal either side of half-time gave their visitors a 2-1 win at the Aviva Stadium, with Jon Walters' 78th-minute strike prompting a late, but unsuccessful, fightback.
"I actually thought we created a lot of chances in the game and I genuinely don't know how we lost the match," said O'Neill. "A combination of things - probably poor finishing, some great saves too - but we should have had the game out of sight by half-time. I thought we played really well. There are big moments in matches where you have to really defend stoutly. You might go 10 or 15 minutes and you are coasting and haven't been tested. Then when the big moments come, you have to be stronger."