Television replays showed that Aguero was fouled in the box by Jose Fonte early in Sunday's game, but referee Mike Jones handed him a yellow card for simulation rather than award a penalty.
Fortunately for City, they recovered to secure a convincing victory, courtesy of second-half goals from Yaya Toure, Frank Lampard and Gael Clichy.
But Pellegrini felt the need to publicly back his star forward in his post-match media conference, while also refusing to condemn Jones.
"I thought it was a penalty, but one thing I was sure of is that Sergio never dived," said the Chilean. "He is not a player who ever tries to cheat the referee and only fell down because of a kick.
"But given the way we won after that decision, it is not important. The referee made a mistake and nothing more.
"If we had drawn 0-0 we'd be talking more about it, but the referee is a human person and everyone can make a mistake."
City also had to overcome the dismissal of Eliaquim Mangala when only 1-0 up, and Pellegrini had no complaints over the French defender's two bookings.
"It was a correct decision," he added. "He had already had another yellow card and it was a foul when they may have scored.
"But I was glad that with 10 men we still tried to score again and didn't look to just stay in our own half."
City could face problems at centre-half for Wednesday's trip to Sunderland, with Mangala now suspended and captain Vincent Kompany limping off late on.
"Kompany has a problem with his hamstring but we'll see tomorrow if it's a cramp or just an injury," continued Pellegrini.
"I didn't see the incident but he was already telling us he had a problem with his hamstring a minute before."
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