"Marko had a small problem behind his knee in the last game," Pellegrini told a news conference on Thursday.
"In the last game (against Arsenal) he was not comfortable to play the final minutes, but he has had all the examinations with the doctor and worked the whole week."
West Ham are still searching for their first points of the season having fallen to defeats against Liverpool, Bournemouth and Arsenal this month.
They have scored just two goals during their sluggish start to the league campaign, both by Arnautovic, but Pellegrini saw signs of improvement as his team came back from a goal down to put away Wimbledon.
"It's not easy to do it, I can give you examples when League One teams have beaten Premier League teams," Pellegrini added.
"We continued believing in ourselves, despite going a goal behind, and they defended very well."
The former Manchester City manager said he does not feel any added pressure despite being rooted to the bottom of the league standings.
"If we started this season by winning three games, the pressure would be exactly the same for the next game," Pellegrini said.
"The pressure from the media can increase when you have no points but for me, the pressure is always the same."
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
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