Arnautovic was forced off with what appeared to be a hamstring injury just before half-time in the comfotable 3-1 win over Cardif fon Tuesday night, with Perez coming on to replace him.
The Spaniard certainly staked his claim, netting twice to fire his side to victory with his first Premier League goals in almost two years.
Now, with Arnautovic facing a spell on the sidelines, Pellegrini says it is up to former Arsenal striker Perez to prove that he can step up and be West Ham's main man.
"It's very important for the team as we won the game," said the Chilean at full-time. "After that for different reasons as he hasn't started much before this game. The important thing is to have options. It's unfortunate for Arnautovic - I hope that he [Perez] continues."
Perez has yet to start a Premier League game so far this season, though his brace against the 'Bluebirds' mean his overall record this term now reads four goals in just 360 minutes of action spread over nine games,
Meanwhile, Pellegrini praised his side for the way they stuck to their task against a difficult Cardiff side to face.
"We improve a lot in the second half. It was a relief. The goal relieved the pressure. That's why we scored two more goals," he explained.
"Cardiff are a difficult team - they only lost 1-0 against Tottenham and Everton. They work very well in the style they like to play."