The Hammers progressed to the third round of the Carabao Cup with a 2-0 win, with Wilshere opening the scoring just before half-time before Pablo Fornals sealed victory in the second half.
And manager Pellegrini believes that Wilshere will get better and better if he stays fit.
“The way Jack continues working every day and playing in games, he will continue improving his performance,” Pellegrini said.
“You cannot expect that he will be the top player when he plays so few minutes last season.
“But in the way he is playing he is demonstrating the good player that he is.”
Wilshere arrived in East London on a free last summer but endured an injury-troubled first season, and has not played a full 90 minutes in over a year.
He started West Ham’s first two Premier League games but did not figure in their 3-1 win over Watford as captain Mark Noble returned from injury with a goal.
Pellegrini suffered another injury setback during the second round win as Michail Antonio limped off with what appeared to be a serious hamstring injury.
The Chilean manager did not know the severity of the issue, but suggested Antonio would miss this Saturday’s game against Norwich and would be re-evaluated after the international break.
“We have the international break after the game on Saturday so after 15 days we will see how big the injury is and we will know how long he is out for,” said Pellegrini.
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