Centre-half Mohsni was red carded for the third time in seven months for aiming a diving headbutt at an opposing player at Pride Park on Saturday.
Minutes after he had gifted possession to the home team before their second goal, he reacted foolishly to a shoulder charge by Scotland internationalist Chris Martin. He lunged at Martin, who had scored both of his side's goals in the comfortable 2-0 victory, and was immediately sent off by referee Mark Heywood.
The French-Tunisian defender could now be suspended for the Petrofac Training Cup game against Hibernian at Ibrox tomorrow night and the SPFL Championship opener with Hearts at Ibrox on Sunday. His fate depends on whether the English Football Association report the incident to their Scottish counterparts. If they do, he will be banned for two games.
Ally McCoist, the Rangers manager, will this week speak to his player about his impetuousness - the umpteenth occasion he has been forced to do so since his arrival in Scotland last summer.
Aird, who made his comeback from a knee injury at the weekend, believes Mohsni will be an important player for Rangers in the second tier and is optimistic he will be able to conquer his demons. However, the winger acknowledged that the League 1 champions can ill afford to lose players against full-time opponents as Rangers bid to win the title and join the SPFL Premiership.
"Big Bilel has been brilliant for us," said Aird. "He was good last year and hopefully he will be good again this year. I am sure he can put what happened today behind him and look ahead. It was hard against Derby with a full team. When we went down to 10 they just kept the ball away from us. It put them on easy street. You need to keep everyone on the park to win games."
Aird squandered an excellent chance to score against Derby after 14 minutes when he headed a Kenny Miller cross wide of goal from a few yards out. But it is doubtful the final outcome would have been different if he had scored.
The huge gulf in class between Steve McLaren's side - who missed out on promotion to the Barclays Premier League in the play-off final last season - and their visitors was evident to every one of the 10,000-strong travelling support.
"Derby were good," said Aird. "They moved the ball about very well. To be honest, I don't think we'll play anyone as good as them this season. They were a lot sharper on the ball. They played a lot of one and two-touch stuff and didn't hang about in possession. I think that is the level we should aspire to. That and even higher if possible.
"Playing against teams like this is always tough. It showed us where we want to take the club. We'll go away and work on a few things, and hopefully bring them into our game at the start of the season.
"We could have been a lot better. I had a good chance to score and we had other chances from corners. I think the boys are ready and looking forward to the season proper starting on Tuesday night."
Despite the one-sided defeat in the East Midlands, Aird was adamant that Rangers are in decent shape ahead of their opening competitive fixtures.
He said: "All the boys are sharp. The lads who have come in this summer have got games under their belt and they look ready. They are fitting into the gaffer's system. Now we just want to put in a good performance to kick off our season.
"Both Hibs and Hearts came down from the Premier League last season. They have lost a few but they have also brought in some. We are looking forward to it and hopefully we can get the results we want."