The Northern Irishman, who first managed Celtic from 2000-05, explained his latest return to the club came in “very similar circumstances again”.
“Obviously, the results just recently for the football club haven’t been great but even though it was still a bit of a shock,” he said.
“Very, very difficult to say no to the man who put me in charge a way back 25 years ago [major shareholder Dermot Desmond].”
O’Neill, who will again be assisted by Shaun Maloney and Stephen McManus, insists he “genuinely” does not know what went wrong under Nancy and also played down the prospect of an extended spell as Celtic manager.
“I can’t see that for a start,” he said. “I genuinely can’t. I don’t know whether I would have the energy and all that type of stuff.
“I’ll just put everything into it now for these next couple of months and the same applies to me – if I don’t win football matches, I’ll be under the same pressure and that starts here at the weekend.”