The French full-back has been widely condemned for his actions during the championship showdown at Parkhead, when he was dismissed for two bookable offences.
Mahe was enraged after he was fouled by Rangers' match-winner Neil McCann and was shown the red card by the referee, Hugh Dallas, as he remonstrated with the World Cup official. He then refused to leave the field, having to be dragged off in tears.
His actions sparked angry scenes from the Celtic fans as they pelted the Rangers players with missiles, and Dallas needed four stitches in a head wound after being hit by a coin thrown from the stands.
Initially, Mahe remained unrepentant, insisting that he had done nothing wrong and did not deserve the punishment which had been meted out.
He claimed the problems had all been caused by Dallas, whose performance he described as "not very good".
However, after a lengthy meeting with the Celtic chief executive, Allan MacDonald, Mahe has changed his opinion.
Together with his Norwegian team-mate, Vidar Riseth, Mahe has publicly apologised for his conduct during the game, agreeing it was unacceptable.
"Allan MacDonald has made it clear in the strongest terms that the club will not accept anything other than the highest standards of behaviour from its players," Mahe said. "I have been heavily fined and seriously censured by the Club, which I fully accept and respect.
"I would like to make a full apology to the Celtic supporters, my fellow players, the Celtic management, the match officials and the general public for my behaviour, which I fully acknowledge was unacceptable. I can only ask for people's forgiveness."
Both men are believed to have been fined two weeks' wages and will automatically miss Saturday's trip to Dunfermline.
They must now await Tuesday's Scottish Football Association hearing into the debacle to see whether they will face further punishment.
It would appear that there will be no apology forthcoming from the third man dismissed on Sunday, Rangers' Rod Wallace.
The Rangers coach, Dick Advocaat, was not at Ibrox yesterday but a club spokesman said that a statement from the former Leeds striker was "highly unlikely".
Riseth, who admitted after the game that he deserved to be dismissed for his last-minute lunge on Claudio Reyna, also expressed his regret.
He said: "Allan MacDonald has left me in no doubt that, on Sunday, I failed to meet the high standards Celtic demands of its players.
"I have been fined and censured, which I recognise is appropriate. Once again, I apologise for my behaviour."
Hugh Dallas, meanwhile, has this weekend off to contemplate the stormy events at the Old Firm match.
Scotland's leading whistle-blower has spent the past three days talking about the controversial game during which, apart from having to send three men off, he was struck by a coin thrown from the stand and awarded a debatable penalty. After the match his house was attacked by an angry Celtic fan.
Dallas has not been given a game in either the Scottish Premier League or Football League this weekend.
Celtic have pruned their expanding squad by deciding to release 11 players whose contracts expire in the summer.
Gerry Crossley, who made his Republic of Ireland debut against Mexico last season, is among the men released, most of whom are Under-21 regulars.
Joining Crossley on their way through the Parkhead exit door are Graeme Morrison, Peter MacDonald, Paul Borland, Brian Vaugh, Marc Anthony, John Potter, Gary Nicol, Stephen Murray, Joe Hayes and Scott Kellagher.
"The standard of player at Celtic right now is higher than it has been in quite some time and that has made their tasks more difficult," the assistant coach, Eric Black, said.