The Ukrainian was a summer signing from German outfit Borussia Dortmund but he only made his first start of the season against Everton last Sunday.
Yarmolenko made an instant impact, scoring an impressive brace to help West Ham to a 3-1 victory at Everton – their first three points of the season.
The 28-year-old’s display led to questions from supporters as to why he had not sooner been given the opportunity to impress from the start in the Hammers starting XI.
But Pellegrini, who also moved to the London Stadium in the summer, has now explained why it has taken him this long to introduce him to the fold.
“I said at the start that Andriy needs a few weeks to get used to playing in the Premier League,” said the Chilean.
“He has a lot of quality, we know that, but in this league you can’t just play with quality. You need pace and be prepared tactically to be an important part of the game.
“He demonstrated against Everton that it was the correct moment. He did it very well. After this performance, we must demand him to give more, because he’s able to be a top player for us.”
Yarmolenko will hope to make his first home start when Chelsea travel across London on Sunday, having previously appeared off the substitutes’ bench against Bournemouth and Wolves on home turf.
Yarmolenko scored six times in 26 appearances for Borussia Dortmund in the 2017/18 season.
Pellegrini also remains hopeful that talisman Marko Arnautovic will recover from injury in time for Sunday’s encounter with Chelsea.
The Austrian is struggling with a knock to his knee but his manager is hopeful the attacker will be available.
“Marko finished with a problem behind his knee against Everton,” Pellegrini said. “He’s having some treatment and we will see if he can be fit for Sunday.
“I think Marko played very well against Everton and we hope he will have recovered for the next game.”
One man certainly missing tomorrow is midfielder Jack Wilshere, following surgery on an ankle injury. Striker Javier Hernandez is also a doubt with a virus.