Arnautovic was red-carded late on in last week's World Cup qualifier away to Sweden, which the Austrians lost 2-1, after a coming-together of heads between him and the hosts' striker Johan Elmander.
Elmander, currently on loan at Norwich from Galatasaray, went to ground in the incident, but replays appeared to show he had thrown himself to the turf theatrically and he was later quoted as saying: "I'm not proud of what I did."
Arnautovic, who has put in some bright performances for Stoke since joining from Werder Bremen in August, arrived in England with a bad-boy image - which he acknowledged this week in an interview.
He also signalled his hope to put it behind him, and when asked on Friday if he had been concerned by what he had seen from Arnautovic in last week's incident, Hughes said: "No, not at all.
"The boy Elmander is probably a little bit embarrassed about his actions that led to Marko getting sent off.
"Maybe his reputation went before him somewhat. It certainly didn't warrant a red card."
There have been various stories over the years about indiscipline on Arnautovic's part and in this week's interview, the 24-year-old admitted he has "done some wrong things".
But he also made clear his happiness with his present situation, as well as his desire, for the sake of his family, to steer clear of further negative headlines.
And certainly it seems Hughes has had no reason to complain about Arnautovic in the time he has been managing him.
Hughes said: "I think Marko, since he has been here, has impressed everybody with his attitude and application.
"He is going to be a big player for us this year. I think his ability is there for everybody to see.
"I think his discipline, in terms of what I ask him to do, and his attacking threat and defensive work are good.
"People possibly like to seek the bad in him.
"But I'd like to think if he keeps performing for us, then people will be more impressed with what he can produce on the field of play rather than what has gone on before, when he was a young man."
Hughes was speaking ahead of his 16th-placed side's home Barclays Premier League clash with 12th-placed West Brom on Saturday, which Stoke go into off the back of three straight top-flight defeats.
The Welshman felt the Potters were unlucky in their last outing, a 1-0 loss at Fulham, and the Staffordshire outfit have subsequently been in contact with Mike Riley at the Professional Game Match Officials Board about the performance of referee Roger East during the contest at Craven Cottage.
Asked about that on Friday, Hughes said: "There have been a couple of conversations about his performance.
"Referees are human and it's not always possible to perform at the level you know you are capable of.
"On the day, he had a bad day at the office and we were a little bit disappointed in his performance and his assistants.
"But we have Howard Webb this week, so maybe that is an illustration that maybe some other people recognised it as well.
"It was a difficult day for the referee and, as a manager, you just want them to get the key decisions in games correct - that is all you want from the officials.
"As long as they get those game-defining decisions correct, then you have no problem. But unfortunately, there was a number of decisions on the day that he didn't quite get right."
Geoff Cameron (calf) is Stoke's only doubt for the meeting with West Brom, whose boss Steve Clarke was a team-mate of Hughes' at Chelsea.
The Baggies have had some notable results of late, with their last two league games seeing them win 2-1 at Manchester United and then draw 1-1 at home with Arsenal.