Marcos Rojo remains injured for United, while fellow South American Alexis Sanchez is out of favour having not even made the matchday squad against West Ham on Saturday despite reportedly being fit.
As for Mourinho, Arnautovic added: "I have nothing to say".
The report indicates that the January signing from Arsenal - allegedly the English top flight's best-paid player on £350,000 a week - is already regretting his move between clubs.
West Ham's Marko Arnautovic celebrates scoring their third goal.
Neville, however, feels Mourinho is not the man to blame for the club's problems and feels their issues can be traced back to the dismissal of David Moyes in 2014.
Mourinho also defended his players from accusations of not trying hard enough, but believes some are taking a slump in form more to heart than others. "We didn't look like a team that was going to beat West Ham".More news: Plane overshot runway before ending up in Micronesian lagoon
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Manager Jose Mourinho said some of his players "care more than others" in his pre-match news conference when asked about the winless run. "It was not good enough from a Man United team with all the talent we have".
They are 14th in La Liga with just one win in their opening seven games but have only lost once.
They welcome Valencia in the Champions League on Tuesday and then host Newcastle United in the Premier League in what could be a huge week for the club. "That didn't happen. It's disappointing and a very, very bad day for us".
"Ask the guy behind you, he was the one who wrote it", Mourinho responded, referring to Sun journalist Neil Custis. He's there to put a team out and put a team out that he thinks can win the game.
"It doesn't matter how they set up, our game was to try to win, we have to do our job and we did it excellently, and that is why we deserved to win", he said. "I understand your frustrations". Of course, we spoke between us and we know the situation is not good and that we can do better.