Turkey were triumphant on their trip to Dublin, with goals from Ahmet Ilhan Ozek and substitute Tarik Camdal providing the platform for victory at Aviva Stadium.
Stoke City striker Jon Walters pulled a goal back for Ireland with 12 minutes remaining, though it was not enough to prevent the nation's second successive defeat on home soil following their loss to Serbia in March.
It could have been a lot different for Ireland had they capitalised on a number of chances, according to a baffled O'Neill.
"I actually thought that 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 cost us. Probably poor finishing, some great saves by the goalkeeper too, but we should have had the game out of sight by half-time.
"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."
Despite the loss, there were a number of positives, including the performance of Wes Hoolahan.
The veteran midfielder, who recently experienced relegation from the Premier League with Norwich City, received special praise from O'Neill.
"I thought little Hoolahan played brilliantly for us. He tried to create things for us during the course of the game," he said.
"Sometimes some big boots come in and shove him off the ball a little bit, but overall he showed a great determination and great ability to try to manoeuvre it.
"He was excellent for us."
