Wilshere came within eight minutes of ending that run as he was substituted in the 82nd minute, but he set West Ham on the path to a 2-0 victory by opening the scoring just before half-time.

"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."

Spanish forward Pablo Fornals, a £24million summer arrival from Villarreal, also scored his first West Ham goal after 65 minutes to secure victory.

But there was a sour note to the Hammers' win, with Michail Antonio leaving the action after seven minutes after pulling up when through on goal.

"He has a hamstring injury, we will see," Pellegrini said.

"I'm happy for the result, happy not to concede goals and happy with the performance, especially the last 45 minutes.

"I think that we dominated the second half. The first 45 minutes was more equal because we knew before that Newport are a difficult team here.

"They have a such a direct style, with so many crosses, but I think that we played a good game.

"A lot of time in this kind of game you start to think that because it's League Two it will be an easy game.

"You normally lose those games when you think like that, so the attitude of the players was very good."

Newport manager Michael Flynn felt his side had let themselves down at both ends of the pitch.

"I thought they were very good but you can't make those mistakes like we did for the two goals," Flynn said.

"The first one with Kyle (Howkins), then Scot (Bennett), and you can't afford to miss the chances we had.

"We had two sitters. Score first and it's a different game.

"It's always nice when Mr Pellegrini says how impressed he was with our team. But you still want to win those games."