Rosler's first game in charge of the Latics ended in disappointment as a 2-1 defeat by Maribor in Slovenia on Thursday night brought the curtain down on their maiden European campaign.
The visitors led through Jordi Gomez's 41st-minute penalty but moments later, Maribor won their own penalty when Chris McCann was deemed to have handled Damjan Bohar's shot.
Marciniak showed McCann a second yellow card and, although Scott Carson tipped Dejan Mezga's spot-kick onto the post, the same player got to the rebound first to score.
Zeljko Filipovic grabbed the winner in the 59th minute with a superb strike into the top corner to ensure it was Maribor and not Wigan who progressed to the last 32.
Rosler said: "It was a deflected ball that led to a penalty, which could be discussed, but even worse was it leading to a sending-off.
"He shot from a very close distance onto his thigh and from his thigh the ball bounced onto his arm. First of all, it's not a penalty for me, and second of all, never a sending-off.
"I think the referee didn't have his best day, he influenced the game in a massive way. He looked to me very inexperienced, he made a lot of errors.
"I can only say I'm very proud of my players, not only with the way they played but they never gave up. We attacked more and in the last minutes it was one-way traffic.
"I think everybody in the stadium would agree that we were the far better team. With no sending-off, we would have won the game."
Marciniak laid out his stall early with bookings for Roger Espinoza and McCann, but Rosler added: "I didn't have a good feeling, and not when the referee gave the two yellow cards but when the game started.
"My players deserved better, that's all I can say about the referee."
It was a sixth consecutive defeat in all competitions for Wigan, who must pick themselves up for a derby clash with Bolton in the Sky Bet Championship on Sunday.
Rosler's desire to return to something like the passing football of Coyle's predecessor Roberto Martinez was evident from the opening moments, and the former Manchester City striker had nothing but praise for his players.
He said: "(The sending-off) wasn't a turning point in terms of performance because we controlled the game after that as well.
"I'm very happy with the way we performed. I think my team did exactly what we wanted them to do and totally dominated the game. I couldn't see them scoring goals.
"We didn't pass the ball in our own half most of the time, we passed the ball in the opposition half. We made them run, they got tired.
"In the second half, 11 against 11, we would have created more and more chances."