O'Neill's admission after the 2-0 home win over Motherwell got their Bank of Scotland Premier League defence off to the right start contradicted Hoops chairman Brian Quinn.
United boss Bobby Robson had claimed the Celtic boss had been after the former England striker, but Quinn hit back by claiming it was Shearer and his agent who had approached the Glasgow side first.
However, after watching his side beat Motherwell in their opening game of the season, O'Neill revealed he had targeted Shearer as a possible replacement for Henrik Larsson.
O'Neill said: "I think what sometimes happens is that I don't relay the messages properly to the board. I was making inroads. We've lost a quality centre-forward and we'd like to replace him with a top-class player. I might as well start at the top and work my way down. Not that I want to argue with the chairman, but I made the initial conversation with Mr Robson.
O'Neill revealed he had looked at several players in his bid to replace the Swedish hitman.
"I've enquired about a number of players and it seems to be drawing a lot of people's attention, but I made an enquiry about a centre forward who has been a top-class player for 13 or 14 years," he said.
"I think Bobby Robson said it didn't get too far but I might as well enquire," said the Celtic coach. "If I don't enquire I'll never know, and it is as simple as that. As Bobby Robson said 'no', that's the end of the story."
O'Neill was reluctant to discuss the possible signing of Middlesbrough midfielder Juninho who has also been linked with the Parkhead club. The Premiership side confirmed Celtic were interested but the Irishman said: "I've been looking to strengthen the side and I will continue to do so right up until the August deadline, and it's only fair that I try to do this because we're embarking on a Champions League which will be exceptionally difficult".
One new face who will be making an appearance for Celtic is Lens midfielder Charles-Edouard Coridon who will face Spurs at Parkhead in tomorrow's friendly during a period on trial with the Hoops. The only downside for Celtic in a comfortable win against the Fir Park men was the injury to midfielder Stilian Petrov who was carried off in the second half with an ankle problem. However, an optimistic O'Neill played down the injury and said: "He was carried off as a precaution and he is in better spirits now than he was at the end of the game.
"He went over on his ankle and we will scan it, but we hope he will be okay."
Motherwell manager Terry Butcher refused to be too depressed about his side's performance despite his players never really looking as if they had the belief to take anything from the champions.
He said: "I thought we started off quite brightly and held them for eight minutes which is probably a record at Celtic Park, so there were some good things to come out of the game."
: Marshall, McNamara, Varga, Valgaeren, Agathe, McGeady (Pearson 74), Lennon, Petrov (Sylla 88), Thompson, Hartson (Camara 67), Sutton.
: Marshall, Corrigan, Kinniburgh, Craigan, Hammell, O'Donnell, Leitch, Fagan (Fitzpatrick 71), Paterson, Burns (Foran 60), Clarkson (Scott McDonald 60).
: K Clark (Scotland).