O’Neill, 73, said he had only had a “10 or 15-minute conversation” with the “affable” Nancy as the changeover took place earlier this month.
The Frenchman endured home losses to Scottish Premiership leaders Hearts and Europa League opponents Roma before Sunday’s 3-1 cup final defeat.
“I stepped into the job, [major shareholder] Dermot [Desmond] had said to me, he said, ‘you could be in it two weeks or two months, we’re looking for someone’,” O’Neill explained.
“When you get into it, you really enjoy it. You enjoy winning, that’s the point – this is what it’s about.
“You’ve got to give managers chances. I think back to my own time at Leicester City, where I eventually enjoyed nice success. Can’t win a game to save my life, crowd baying for blood and after 10 games. How lucky I was to win a couple of matches of real importance at a stage.
“You’ve just got to win, you’ve got to win. You’ve got to steady it again. There’s some excellent players at the football club. There’s some boys who have won big time as well. Lean on some of the senior players. Lean on them and get them on your side.
“It is recoverable, of course. You’re in the football club 10 or 12 days.
“You cannot make a judgement on anybody over three games. The matches were difficult. You have got to give a manager some time.”
