The Premier League title challengers were put to the sword by Tata Martino's side, with Lionel Messi converting from the penalty spot following a cynical foul by Martin Demichelis before Dani Alves sealed the win in the closing moments of the match.
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He told Sky Sports: "Of course I have a complaint, and not only for the penalty and the red card. In the whole match I didn't feel we had a referee with impartiality to both teams, and he decided the game.
"He decided the game because it was a foul by Busquets on Navas. He was three metres away but didn't want to whistle, and the foul by Demichelis outside the box is not a penalty.
"With such important mistakes against a team as great as Barcelona, it's very difficult to win.
"I think it's a mistake to nominate a referee who had problems with Barcelona [turned down penalty appeals vs AC Milan last year] as the referee here, and I repeat he decided the game."
Reflecting on whether his side can turn things around and advance to the quarter-final stage of the competition, Pellegrini accepts it will be a tough ask but holds out hope that a comeback could still be possible.
He added: "Of course we are going to try. We are going to play in Camp Nou. We did it against Bayern after we lost at home. The second goal was a difficult moment because the match was ending and now they have a two-goal advantage, but we will see what we can do there."