City fell behind in their last-16 first-leg clash when Eriksson awarded a penalty to the visitors in the 53rd minute for a foul by Martin Demichelis on fellow Argentine Lionel Messi that appeared to take place outside the area.
To compound the punishment, Demichelis was sent off, leaving City to play the rest of the match down to 10-men, with Messi firing home from the spot and Dani Alves adding a second goal in stoppage time.
Chilean Pellegrini, who normally keeps his own counsel, was highly critical of the Swedish official, who has held a FIFA badge for 12 years and has now refereed 22 Champions League and 87 UEFA matches in total.
Pellegrini, who risks a severe sanction from European football's governing body, said: "I spoke to him (Eriksson) at the end and told him he should be very happy because he decided the match.
"Barcelona had no chance to score until the penalty against Demichelis.
"The referee was not impartial. He did not have any control of the game. I think it was not a good idea to have a referee from Sweden in such an important match.
"He did not call for a foul on (Jesus) Navas before the penalty. On the penalty, the foul was made outside the box, but more importantly we were building up the play.
"The first mistake was not giving a foul against Navas and then deciding it was a penalty when it was not a penalty.
"But it was not the only thing, he made mistakes from the beginning. It is very difficult to analyse the game because of that."
Asked why it was relevant that the referee was Swedish, Pellegrini replied: "More important football is played in Europe than in Sweden so a big game with two important teams - that kind of game needs a referee with more experience."
Pellegrini was also angry that Eriksson had been chosen for Tuesday's match after he had previously dismissed two Barcelona penalty claims in the 2012 Champions League quarter-final against AC Milan at the San Siro.
"I think it's a mistake to nominate a referee who has mistakes against Barcelona to have the same referee here," he told Sky Sports. "I say once again he (the referee) decided the game."
- Sports & Recreation
- Martin Demichelis
- Champions League
- Lionel Messi