Pellegrini said Eriksson was "on Barcelona's side from beginning to end" during City's 2-0 loss at the Etihad and was trying to make up for a previous mistake against the Catalan side, and also questioned UEFA's decision to appoint an official from Sweden for the Champions League last 16 first leg match.
UEFA is likely to take a dim view of such comments - in 2011 it banned Jose Mourinho for five matches, reduced on appeal to three, for a similar rant when he was at Real Madrid.
Pellegrini's comments overshadowed a game which was decided by Lionel Messi's penalty, which led to Martin Demichelis' dismissal, and Dani Alves' last-minute strike.
The City manager claimed the foul by Demichelis was outside the box and that Eriksson - who has been selected by FIFA as one of the referees for this summer's World Cup in Brazil - should have given City a free-kick earlier in the move for a challenge on Jesus Navas by Sergio Busquets.
He said: "From the beginning I felt the referee was not impartial so he decided the game with a foul that he didn't whistle against and a penalty with Demichelis that was not a penalty, it was outside the box.
"He did not have any control of the game. He was on the side of Barcelona from the beginning until the end.
"I think it was not a good idea to put a referee from Sweden in charge of such an important match, especially a referee who has made an important mistake against Barcelona in a previous match."
Pellegrini appeared to be referring to the 2012 Champions League quarter-final, when Eriksson was criticised by then-Barcelona coach Pep Guardiola for failing to award his side two penalties.
"This referee whistled the Barcelona-Milan and he made an important error against Barcelona. Today he rearranged it," said the City boss.
Captain Vincent Kompany also claimed after the game that Barca were "in no way superior" to City and had been "there for the taking".
That, coupled with Pellegrini's outburst, led television pundit and former Manchester United defender Gary Neville to write on Twitter: "Not a personal criticism but City displaying the reaction and hurt that comes with immaturity in Europe!"
Cesc Fabregas, meanwhile, was delighted his Barcelona side could "prove a point" after Chelsea boss Jose Mourinho called the Catalan side "the worst Barcelona of many years".
Fabregas told ITV: "Maybe we had to prove a point in a way and I think we did it very, very well, but this team has done too much and won too much to always have to prove a point.
"Maybe everyone was saying Barcelona was not the same Barcelona...some people were talking a bit too much and as usual they will have to shut up for a few days.
"We are top of the league, we had a good result and we are in the final of the [Copa del Rey]. There's nothing else you can ask for."