Arnautovic scored twice as West Ham swept aside Southampton 3-0 on Saturday.
"Marko has had a special season but he finished very well today," said Pellegrini. “Next season, I am sure we are going to see the Marko Arnautovic who knows how much he can give to this club.
“Today, he played very well, not just with the two goals that he scored but also with the way he was involved in the game. He was absolutely concentrated.
“We hope we can have a complete season from Marko Arnautovic in the way he played today."