City suffered another set-back in the Premier League title race with the costly defeat at the Etihad Stadium - their seventh of the league campaign.
Harry Kane opened the scoring with the controversial penalty early in the second half after Danny Rose's cross had deflected off Sterling's back and onto his elbow, with Clattenburg pointing to the spot.
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City substitute Kelechi Iheanacho looked to have salvaged a point, but Christian Eriksen's winner seven minutes from time proved decisive and Pellegrini was left to rue the penalty decision.
"Before the penalty we had more clear chances. There were not too many in such a close game but the penalty was very important," he told Sky Sports.
"Unfortunately it is the same referee who in the first game against Tottenham earlier this season gave two offside goals. It's an unbelievable penalty that decides the game.
"The shot hits the back of Sterling then his elbow slightly. I don't think the referee can decide the game in that way. That action in such a close game was absolutely decisive.
"We are very unlucky with this referee, we have nothing more to do than to complain about that action."
City currently sit six points behind league leaders Leicester, to whom they lost last week, while Tottenham and Arsenal occupy second and third respectively - separated only by goal difference.
Asked about his side's fading title chances, Pellegrini added: "We responded well but I feel it was more important to win the three points.
"We are not going to give up, losing twice here against Leicester and Tottenham is too much but we have to continue working with the players.
"The spirit of the team was very good, we need to improve our football but we are going to carry on fighting as far as we can."