Two goals behind at the break, the visitors rallied in the second 45 as goals from Sebastian Tounekti, Benjamin Nygren, and Julian Araujo proved crucial.
“It’s both worrying me and, well, it’s not great for my health,” O’Neill said post-match. “Overall, if that’s the way you have to win the games, you have to win them like that, but I agree, you just can’t keep doing that.
“Sometimes I wonder how they got themselves into this position in the first place.
“You can throw all the usual accolades around, but they deserve them today because even at half time, when we were so, from my viewpoint, I thought we were poor, I thought that there was still that feeling that we could turn it around if we could get a relatively early goal in the second half, and that’s what happened, so getting back to your point, it’s great to see it.
“Twenty-odd years ago, I managed a really fine team, who had loads of spirit, loads of determination, all saw it to the end. There were many traits here about this side, they’ve shown fantastic character, really from a poor first half, from our viewpoint, strong Kilmarnock, 2-0 down at halftime, and they never gave up.”
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O’Neill rang the changes at the break against Kilmarnock, replacing Yang Hyun-jun, Reo Hatate, and Junior Adamu with Tounekti, Alex Oxlade-Chamberlain, and Tomas Cvancara.
“Could we have made seven changes at the time?” the Celtic manager joked. “Sebastian Tounekti comes on, scores a great goal, gives us a little bit of width, he’s going to take people on, on that side.
“I had thought about maybe starting Alex Oxlade-Chamberlain, I’m not sure in terms of fitness and things I guess here, he’s come on, he’s just a class player, an absolutely class player.
“Big Tomas Cvancara comes on, what a turn for the final goal, so it was great to see them making big impacts in the second half.”
Right-back Araujo came up trumps for Celtic in the final minute of stoppage time, slamming home at the back post to spark raucous scenes in the Rugby Park away end.
“There were periods in the first half where I would have retracted what I said, you know, but he did great,” O’Neill once more joked. “For him to arrive there in the box at that time, I’m still having to, I haven’t seen it back first time, but some of the lads are telling me he still had to put it into the net, so well done him, he made up for some of his first half recklessness.”
O’Neill confirmed that midfielder Arne Engels will be sidelined with a thigh injury until the end of March, an undoubted blow ahead of a Europa League tie against Stuttgart, the first leg of which comes on Thursday evening.
“If I want to be really honest about it, there are some big, big teams that are still in that competition, and it’s a long way from home as well,” O’Neill continued. “Home meaning a long way to go. Even if you went through against Stuttgart, who are in the Bundesliga, you’re still talking about into the last 16. That seems like miles away.
“So this is like the last 24. If it was a bit closer, you know, then you can think about it. It’s just, we’ll see what the energy’s like.
“But having said this, I wouldn’t want to give it up, just wouldn’t want to, you know, you’d like to, but the coefficient eventually might help Scotland at some stage, you know. Long after I’m gone!”