"We lost the game," said Pellegrini. "You are frustrated and angry.
Manuel Pellegrini criticises referee Eriksson
"Maybe I said something but I don't think that way. I want to apologise."
Pellegrini's side were reduced to 10 men when Martin Demichelis was dismissed for denying Lionel Messi a clear goalscoring opportunity. The Argentine scored from the resulting penalty.
The initial contact appeared to take place outside the penalty area and followed what Pellegrini believed to have been a foul by Sergio Busquets on City winger Jesus Navas.
"I didn't say he was a bad referee, that he was not honest, that he cannot referee in Uefa," said Pellegrini, 60.
"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."
After Daniel Alves added to Messi's opener to give Barca a two-goal advantage ahead of the second leg of their last-16 Champions League tie, Pellegrini questioned why a referee from Sweden was chosen to officiate the match.
BBC Sport's Alistair Magowan at Pellegrini's news conference
"This was a convincing performance from Manuel Pellegrini, who was keen to apologise not only to referee Swedish Jonas Eriksson but also the official's home nation.
"The City boss looked genuine when he admitted anger got the better of him following his uncharacteristic criticism of Eriksson after the Barcelona defeat. And less than 24 hours after receiving news that he is facing a Uefa investigation for his comments, Pellegrini has attempted to draw a line under the incident. But with a charge now brought against him, it has had little effect."
The former Real Madrid boss also implied Eriksson may have been influenced by the fact he made an error that hindered Barcelona in a previous European tie.
"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," added Pellegrini.
"I am sure this is a good referee because Uefa are 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."
Uefa, football's governing body in Europe, have appointed a disciplinary inspector to review Pellegrini's post-match remarks and could take action if they are deemed inappropriate.
Jim Boyce also defended Eriksson,
insisting it was "absolute nonsense to say a referee should not be chosen because he comes from a smaller country".
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