Villa looked to be coasting to victory - and an eight-point lead over fifth-placed Arsenal - after goals from Stiliyan Petrov and John Carew had put them in total command.
But Stoke, who had posed a bigger threat after the introduction of substitute Ricardo Fuller, stunned the home side with late goals from Ryan Shawcross and Glenn Whelan.
It means Villa have won only five of their 14 home games this season compared with 10 victories in 13 matches away from Villa Park.
O'Neill said: "We were more than disappointed in the dressing room afterwards. In fact, everyone was devastated.
"We were in total control at 2-0 and with five minutes to go you should be able to see a game out.
"It didn't materialise and we have dropped two points. For the first time today I thought there was a degree of over-confidence about us.
"I just felt, having got the second goal, we should have been able to read the situation better and what might develop in the last couple of minutes.
"Once or twice we were still looking to play the sort of intricate football that got us 2-0 up instead of seeing the game out. It is a real disappointment."
O'Neil added: "We were brilliant in the first half and some of our movement was excellent. We started the second half sloppily and didn't get into a rhythm for a while.
"But we got the second goal and were then in complete control. Stoke were left with nothing to lose and were always going to put the ball into our box and we should have been able to deal with it.
"At the moment it is hard to understand why (they only drew). They came here to sit back and I have not got a problem with that. It is up to us to break them down and we did that.
"I think the normal top four sides would have seen it through. Is that a lesson we will learn? I hope you are right.
"There are still plenty of games left and we have won games ourselves in the last minute but to drop two points today is galling because for the most part we were excellent."
Stoke boss Tony Pulis was delighted to pick up a point from a game which appeared to have slipped from their grasp.
He said: "For long periods we were hanging on against a very good Villa side.
"In the first half we were very poor but that was down to me. We tried to eliminate their wide players but it just didn't work.
"We went back to a normal 4-4-2 and it was better in the second half.
"When John Carew scored, you think the game is over but we had five great chances in the second half and this is an important point for us.
"Everyone outside Stoke thinks we are the team that will get relegated. But we think we are going to stay up so the pressure is on everyone else."