Former Brentford boss Rosler took charge of his first Latics game in Slovenia on Thursday night but could not stop his new team sliding to a sixth straight defeat and out of Europe.
There were plenty of encouraging signs for Rosler in the 2-1 defeat by Maribor, though, and had Chris McCann not been harshly sent off in the first half, Wigan may well have won the game and progressed to the last 32 of the Europa League.
Rosler succeeded Owen Coyle on Saturday and McArthur hinted the former Bolton's boss' unpopularity may not just have been with the fans.
Rosler has pledged to reinstate something like the passing style that Wigan were renowned for under FA Cup-winning manager Roberto Martinez, and the change of emphasis was immediately apparent.
McArthur said: "He wants us to pass the ball. We're trying to get back that style that we had before where we were getting it down and passing it sharp. In spells we did that and we can only grow from this."
The key spell of the game was three minutes at the end of the first half.
First Wigan took a deserved lead through Jordi Gomez's penalty but Maribor went straight up the other end and earned a spot-kick of their own.
Latics were furious a penalty had been awarded after McCann blocked a shot with his leg before the ball bounced up and hit his arm.
Worse was to follow from officious referee Szymon Marciniak, who later sent off Maribor's Ales Mertelj, as he showed McCann a second yellow card.
Scott Carson saved Dejan Mezga's penalty but the midfielder tapped in the rebound, and Maribor made their numerical advantage count 14 minutes after the break when Zeljko Filipovic slammed in the winner.
McArthur said of the penalty and red card: "I've not seen it again but I've seen Chris' leg and there's a big ball print on it, so on that evidence it's hard to take really."
Maribor began the day bottom of Group D but victory coupled with defeat for Zulte Waregem against Rubin Kazan sent them through to the last 32 with the Russians.
Wigan had been in a very good position after picking up five points from the first three European games in the club's history.
But a home defeat by Zulte two weeks ago was where it really slipped away, leaving McArthur ruing what might have been.
He said: "It's been a very good experience but it's disappointing to go out at this stage, especially when we had a really good chance. I don't think we've done ourselves justice given the position we were in.
"We only needed to turn one of those results round and it may have been different but there's nothing we can do now. We just need to look to our league form and try to start picking up wins.
"It is very hard to realise that if we won we would have been through, I think that's made the blow a lot worse."
Wigan have no time to dwell on their European exit with a derby clash against Bolton at the DW Stadium on Sunday, where McArthur hopes they can resurrect their faltering promotion bid.
The Scot said: "It is the biggest game of the season, especially because we haven't been picking up wins. It's a derby and we need to try to turn the season round by getting three points and try to start climbing that table."
McArthur, meanwhile, was full of praise for the 1,000 fans who made the trip to Maribor and feels they would have headed home with renewed optimism.
He said: "I think it's the best I've ever seen them. For 1,000 fans they made so much noise and they helped us try to come through, especially with 10 men.
"The good thing for us is they weren't impatient. We were passing the ball side to side and they weren't getting on our backs to try to get it forward and score, I think they appreciated that we were trying to play football again."