Turkey scored twice on the counter-attack in Dublin as the hosts fell 2-0 behind before Jonathan Walters pulled a goal back in the 78th minute.
They couldn't complete the fightback, however, and O'Neill was at a loss to explain how his side didn't have the match wrapped up by half time.
"I actually thought that we created a lot of chances in the game and I genuinely don't know how we lost the match. A combination of things - probably poor finishing, some great saves by the goalkeeper too - but we should have had the game out of sight by half-time," O'Neill told reporters.
"I thought we played really well. I was just saying in the dressing room, there are big moments in matches where you have to really defend stoutly. You might go 10 or 15 minutes in the match and you are coasting through and you haven't been tested. Then when the big moments come, you have to be stronger.
"Eventually we conceded two goals tonight when I think that there should have been less danger. That said, genuinely going forward, I thought we were excellent and somebody is going to earn themselves a fortune by being able to put the ball in the net, an absolute fortune."
The defeat is Ireland's second in a row following their loss to Serbia in March.