They will discover on Thursday whether they will be punished for the ugly scenes that occurred during Wednesday night's 1-1 Group G draw in Bucharest.
Assistant manager McCoist told BBC Scotland: "Ourselves, like many other clubs, have mindless idiots who bring shame on the club.
"The club's doing just about everything possible to deal with these idiots but I don't know if we can do any more."
Television pictures showed a number of travelling fans clashing with Romanian police in the stands during half-time of Wednesday's match, while one supporter was seen to rip out a seat.
Police used CS gas spray in an effort to disperse fans.
Although condemning the minority of fans involved, chief executive Martin Bain insists it was triggered by poor organisation at the Steaua Stadium and over-zealous policing.
He has vowed to argue a strong case in front of UEFA's control and disciplinary body next week.
Bain's explanation was also backed by Superintendent Mike Dean of Strathclyde Police, who was helping to co-ordinate security at the ground on the night.
UEFA appear to have taken this into account after yesterday beginning disciplinary proceedings against Unirea over a "lack of organisation" regarding the entry procedure for spectators at the ground.
But Rangers' previous conduct will also be considered when the control and disciplinary body meet next week.
The club have been fined twice in the last four seasons by European football's governing body over the behaviour of their fans, and manager Walter Smith fears the next punishment could be a ban.
McCoist said: "From our point of view, it's sickening. It's our job as players and coaches to get teams on the park and we don't want to be deprived of that.
"But I watched the thing on television and I saw half a dozen idiots who did their best to shame the club.
"I get a little bit upset about the criticism the club gets but I fully accept they're in with our supporters.
"Hopefully, we'll find them and they won't be watching anyone, never mind Rangers."
In recent years, the Light Blues were fined £13,300 for fans' discriminatory chanting and £9,000 after supporters attacked their opponents' team bus during an away game against Villarreal in 2006.
The following year, they were fined £8,280 on an improper conduct charge for fans' behaviour at an away UEFA Cup game against Osasuna.
Supporters have also been in trouble with police, with the rioting during last year's UEFA Cup final in Manchester regarded as one of the most shameful episodes in the club's recent history.
Already this season, Dinamo Zagreb have been docked three points and ordered to play two Europa League group games behind closed doors after serious crowd disturbances during their game against Romanian side Timisoara.
However, the Croatian club have appealed the punishment.