Slawomir Peszko took advantage of a Robbie Brady error to score what looked like being the winner for Poland midway through the first half.
But Shane Long came off the bench to score in the first minute of stoppage time and secure a share of the spoils.
The draw leaves Ireland fourth in Group D, three points behind leaders Poland and two adrift of Germany and Scotland ahead of the visit of Gordon Strachan's men in June.
"The one thing you can never say against this side is that they lack spirit," O'Neill told RTE.
"We've kept going right until the end. We got a late goal in Georgia, a late goal against Germany, it is not to say we didn't deserve it [but] tonight, we certainly did.
"The second-half performance was fantastic. We had them on the back foot the whole second half and it would have been a shame if we didn't get anything out of the game.
"I thought James McClean gave us that spark, just at that point in the game when we might have felt things were beyond us.
"I am delighted we are still in the competition. We have to beat Scotland in June, and if we show the same determination, same spirit and same ability, then we can do them."
Long added: "That could prove to be a massive point from us. We have already learned our lesson from Scotland and dug deep today to get the point.
"To keep them within touching distance is a big thing for us. We should probably be beating teams at home, but the main thing was not to lose."
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