O’Neill was taking charge for just the second game of his interim spell after Brendan Rodgers resigned on Monday amid acrimonious relations with the club’s board.
Celtic will face St Mirren in the final on Dec 14, but O’Neill, who enjoyed great success during his first spell as manager between 2000 and 2005, expects the permanent appointment of a new boss to be made during an international break later this month.
“Secretly, you would love to,” said the Northern Irishman. “We’re in the results business and all of these things can change.
“I would have thought that with Midtjylland now (in the Europa League) Thursday night and then Kilmarnock on the Sunday, there’s probably time for them, with an international break, for the board to think about something.”
Both sides of the Glasgow divide are under new management after poor starts to the season that has allowed Hearts to open up a nine-point lead in the Scottish Premiership.
Rangers boss Danny Rohl is also less than two weeks into his role and was given another example of the job he has to turn around a side that is 14 points behind Hearts in the league and bottom of the Europa League table.
The struggles of both teams showed in a tepid 0-0 draw in August, but the fire often associated with this fixture was back in abundance at Hampden.
Celtic took the lead midway through the first half when Johnny Kenny headed in Arne Engels’ corner.
The holders appeared on course for a comfortable passage to the final when Thelo Aasgaard was then shown a straight red card for a wild studs-up challenge on Anthony Ralston.
Celtic were lucky not to also be reduced to 10 men before half-time when Auston Trusty caught Rangers goalkeeper Jack Butland on the head.
The unhappy final days of Rodgers’ reign were beset by his frustration at Celtic’s failure to add more quality in the final third during the transfer window.
That flaw remains very much an issue despite the departure of the former Liverpool boss as O’Neill could not contain his frustration at Celtic’s inability to put the game beyond the 10 men in the second period.
A lack of killer instinct came back to haunt the Scottish champions when Ralston was penalised for handball 10 minutes from time.
James Tavernier fired home the resulting penalty to send the game to extra-time.
However, Celtic finally made the man advantage count against a tiring Rangers in the extra 30 minutes.
Butland should have done better when Callum McGregor blasted in from outside the area.
Teenager Callum Osmand then made sure of Celtic’s place in the final when he slid in to meet Kieran Tierney’s cross.