Ireland had captain John O'Shea sent off late on for a second yellow card and O'Neill insists his men have a fighting chance of making it to France.
"It is disappointing because beating Germany (1-0) gave us a run at it," the manager was quoted as saying by the BBC.
"Whoever we play (over two legs in the playoffs), we will have as good a chance as them," he added.
"Before we played Germany if you had offered me third I would have taken it. But that win gave us the confidence to come and play here.
"We had to go for it in the second half, I actually thought we might have got a second goal, and that would have taken us through. Right until the end we were there but we were perhaps lacking that cohesiveness.
"Despite putting a lot of pressure on them it wasn't to be. But we are still in there, we can still make it. We didn't make it but we are still fighting strongly," he added.
The play-off draw takes place on Sunday.
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
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