Martin Demichelis' late header rescued a point for Premier League champions City in Saturday's clash at the Emirates Stadium, after goals from Jack Wilshere and Alexis Sanchez had helped Arsenal cancel out Sergio Aguero's first-half opener.
However, Pellegrini was furious with official Clattenburg following the match, claiming that there were fouls in the build-up to both of Arsenal's goals, while he also felt his side should have had a penalty for a handball against Wilshere.
"I think both goals from Arsenal are clear fouls," he told BT Sport.
"The first there are several fouls on Sergio Aguero. For the second, there was a foul, a clear push on [Vincent] Kompany from [Danny] Welbeck in the box and they scored from the resulting pass.
"We finished with a clear penalty, the ball hitting Wilshere in front of the linesman."
Pellegrini believes it is not the first time that City have fallen foul of a poor decision by Clattenburg, referencing a missed handball against Martin Skrtel in April's 3-2 defeat to Liverpool at Anfield.
"He [Clattenburg] had a bad game and a very bad day against Liverpool last year when Skrtel punched the ball."
Despite his displeasure with Clattenburg's performance, Pellegrini was happy with the way City applied themselves against a Premier League title rival.
"It was a great game," he added. "[It was] two very good teams who like to play and both are very creative teams. It was a good game.
"I am satisfied because I think it would be very difficult to retain the title because all the teams want to beat us. It's hard to play away especially.
"We have more possession, more chances and I'm very satisfied in the way my team played."
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