The Rangers captain made his confession in an official club statement after watching a video of Rangers' defeat on penalties in the Uefa Cup second leg match in Germany on Tuesday. But the Italian defender maintained: "I would like to make it clear I am not a racist."
The Nigerian said after the game that he did not hear what the Italian said and Dortmund do not plan to seek any disciplinary action. Amoruso watched a video of the game yesterday after having Wednesday off with the rest of the squad.
The statement read: "During the game against Borussia Dortmund I was involved in an incident with Victor Ikpeba and words were exchanged between the two of us. However, in a highly-charged football match it is not unusual for tempers to boil over and I do not remember making the remarks attributed to me.
"This morning I viewed the video recording of the game and, on this evidence, I cannot dispute the fact that I made the remarks. I would like to make an unreserved apology to Victor Ikpeba for these comments.
"I would like to make it clear that I am not a racist and deeply regret any upset I have unwittingly caused to the player or anyone else."
Amoruso met the Rangers manager, Dick Advocaat, and the club's director- secretary, Campbell Ogilvie, yesterday but Rangers refused to say whether they would discipline their captain, although they may feel duty bound to take that course of action.
"We discussed the incident at length and it is accepted that the player did not recollect having made these comments," Ogilvie said. "However, on viewing the video recording of the match, the player admits the comments attributed to him were made.
"Lorenzo is not a racist and obviously he very much regrets his actions which took place in the heat of the moment."
The Rangers chairman, David Murray, said yesterday that he is ready to enter the transfer market after the disappointment of his side's Uefa Cup exit. "We are not talking here about players who cost only a million," he said. "Rangers are well down the road to huge signings and they will be of a much better standard than what we have now."