Manuel Pellegrini liked much of what he saw from his West Ham team, despite a third defeat in as many Premier League matches at Arsenal.
Danny Welbeck's stoppage-time clincher means West Ham have now conceded nine times in their three outings under Pellegrini, but the ex-Manchester City manager did not believe the scoreline gave a fair reflection of the action in north London.
"I am not happy with the result but I am very happy with the performance of the team," he told a news conference.
"It was what I demanded of the players. To come here, to Arsenal's stadium, against a big team and to play as a big team and think like a big team.
"We did that during 90 minutes and were very unlucky to concede the own goal that put Arsenal in front, and the last goal when we were trying to equalise in the last minute.
"Soon this team will win more games than we are going to lose. Of course, we need to add points but in each game we have improved a little bit more.
"The result was nothing to do with what happened in the 90 minutes. We created double the chances of Arsenal but two or three balls were decisive."
Felipe Anderson provided West Ham's creative spark in his best display since joining as a record signing from Lazio, linking pleasingly with Arnautovic on a number of occasions.
"Felipe can play in different positions. He played well behind the striker," Pellegrini added. "But not only Felipe, other players did better than the opposition."
On Arnautovic's condition, the West Ham boss added: "We will see during the week. He felt some pain in the muscle behind his knee."