Pellegrini faces possible sanctions from UEFA after saying Eriksson was "not impartial" and questioning why a referee from Sweden had been appointed to the Champions League fixture.
The Chilean also suggested Eriksson was trying to make amends for perceived injustices against Barca in a previous fixture he officiated involving the Spanish champions.
Pellegrini now regrets the comments about Eriksson's nationality and concedes his other complaints were out of character.
City were beaten 2-0 in the first leg of their last-16 tie at the Etihad Stadium with the game hinging on a controversial penalty conceded by Martin Demichelis - who was also sent off - early in the second half.
Pellegrini said: "When you lose a game the way we lost against Barcelona, you are frustrated, you are angry.
"Maybe I said some things I didn't mean so I apologise for what I said.
"Also I want to clarify what I said, I didn't make any serious accusations to anyone, not to the referee, not to UEFA, not to anyone.
"I always say refereeing is a very difficult profession because they have only have a fraction of a second and after people compare their decisions with eight television cameras.
"It is not my way to act to criticise the referee, but in that case it was not a good day and he decided the game - but not with the intention to benefit Barcelona or damage Manchester City. He was in a bad day with very bad luck."
UEFA, the European governing body, has launched an investigation into Pellegrini's comments and will determine in due course whether disciplinary proceedings should follow.
Pellegrini, speaking at a press conference to preview this weekend's Barclays Premier League game with Stoke, addressed each of his complaints.
Attempting to clarify his remarks about Eriksson's impartiality, Pellegrini said: "I felt from the beginning his criteria was not the same for both teams.
"I think he had a bad day - everyone can have a bad day - but I didn't say that intentionally he didn't give fouls for us or did give fouls for Barcelona.
"I said from the beginning it was not the same criteria. I repeat, a bad day, not dishonest."
With regard to Eriksson hailing from Sweden, where the league is not considered as competitive as in some of Europe's leading football nations, Pellegrini admitted he made a mistake.
He said: "To say because he was always refereeing in the Swedish league, and that maybe it was better for so important a game to have another kind of referee - it is another thing I didn't think.
"It is not an offence to Sweden or the Swedish people or referees.
"Sweden is a country that has a lot of good players, they have one of the best in the world in Zlatan Ibrahimovic and it can also have a good referee.
"I am sure this is a good referee because UEFA is always evaluating all the referees and if he is not a good referee, he is not in the UEFA staff.
"The thing I said in that moment doesn't mean what I think.
"I didn't say any serious accusation about Sweden, just that it was not the most important league in Europe and that is not an offence, I think."
On the issue of whether Eriksson favoured Barca to right wrongs from a previous match, Pellegrini said he was thinking aloud in the heat of the moment.
He said: "The third thing I said was that it was not a good idea that a referee that damaged Barcelona against Milan to referee the game, because if the same thing happened in the Barcelona box and Barcelona lost the game 1-0 with that penalty and one player sent off, all around Barcelona they would say the same referee did it again.
"It is my idea. I am not in charge of referees. I think it is important managers do what they have to do, the referees do what they have to do and the staff in charge of deciding the referees do what they have to do.
"I repeat, I didn't have any serious accusation, not against UEFA, not against the referee, not against Sweden, not against anyone.
"So it was my way of thinking and I was angry."