For victory over Huddersfield Town, this was the first time the 29-year-old had started a game since he was linked with a move to Shanghai SIPG at the end of the transfer window.
"The fans are always very loyal," said Pellegrini. "The fans, if a player plays well, they will accept not only Marko Arnautovic but every player.
"The fans want to see their team winning. After that, they want to see the player giving all that they have, after that they want to see quality and if, in this moment, it's not your day, it happens to all players at every club."