City headed into the first leg of their last-16 encounter full of optimism, but now have a mountain to climb in Catalunya if they are to prolong their European adventure.
The Premier League title hopefuls matched Barca for long periods at the Etihad Stadium on Tuesday, creating the better opportunities despite seeing the visitors dominate possession.
The tie was taken away from them, though, early in the second half as Lionel Messi sprung clear and was tripped by the backtracking Martin Demichelis.
Eriksson pointed to the spot and Messi duly converted, but Pellegrini believes Jesus Navas was felled in the build-up to the move which led to the awarding of a penalty and that Demichelis' challenge - which led to him being shown a straight red card - initially took place outside the box.
The City boss, who saw Dani Alves add a second for Barca in the closing stages, told Sky Sports: "Of course I have a complaint, not only for the penalty and the red card.
"I think in the whole match we didn't have a referee with impartiality to both teams.
"He decided the game. He decided the game because it was a foul by (Sergio) Busquets on Navas. The referee was three metres away and he didn't blow the whistle and after that the foul from Demichelis is outside the box, it's not a penalty.
"Important mistakes against a great team like Barcelona make it difficult to win."
Pellegrini says Eriksson should never have been handed the game by UEFA, with the Swedish official having history with Barcelona after turning a deaf ear to their penalty shouts during a last-16 encounter with AC Milan 12 months ago.
He added: "I think it is a mistake to nominate a referee that has had problems with Barcelona.
"Maybe he made mistakes in Milan. To have the same referee here, I repeat, is a mistake."
City will now have to net at least twice at the Nou Camp in three weeks' time, but Pellegrini is refusing to throw in the towel on the Blues' continental campaign.
He said: "We are going to try, of course we will try.
"We are going to play at Camp Nou and we did it against Bayern Munich also after losing at home (in the group stage).
"But of course the second goal came at a difficult moment because the match was ending, it was finished. We will see what we can do."