The Ibrox faithful were criticised after they were caught on camera belting out a string of sectarian anthems and other unacceptable songs during Saturday's Irn-Bru Scottish Football League Third Division match at Berwick.
Club bosses even issued a statement halfway through the Glasgow side's 3-1 win at Shielfield expressing their concern over the chants.
And broadcasters ESPN also made an on-air apology to viewers who were offended by the supporters' actions as they screened the match live.
McCoist have urged fans to "behave" while following the Light Blues but suggested it might help supporters if they were told exactly what songs they were and were not allowed to sing.
He said: "If that eradicates the problem, then I'm all for it - absolutely all for it.
"Anything that would move us forward and eradicate that problem that we had at the weekend would be helpful.
"It might seem like a drastic measure but if it helps, then I don't have a problem with it at all. In fact, I'd encourage it."
UEFA issued Rangers with a 40,000 euros (£35,180) fine and banned its fans from travelling to Sweden for the club's Champions League qualifier against Malmo last season after they were charged with sectarian singing during a Europa League match at PSV Eindhoven in March, 2011.
But McCoist insists the club has been stringent in its work to rid its support of the sectarian element.
"The club has taken giant strides to move forward," he said. "The vast, vast majority are of that opinion and that is what we want.
"There is no place for Saturday's songs in the modern game, we all know that. They are unacceptable and there is no place for them in a modern society.
"We are doing our best to move forward and some massive, massive steps have been taken. The weekend was obviously a disappointment but I'm not going to get too carried away with that disappointment because we want to keep moving forward again.
"I don't have any doubts that the majority of our fans want to leave those days behind us.
"We will move forward, because we have got a phenomenal fan base who have been nothing short of fantastic this season. The vast majority of them know what is expected, because they are representing the club as well.
"It's important that they behave themselves and the club has a good image moving forward.
"I want them to come and sing the songs that get the Rangers team going but support them in the proper manner. That is exactly what we want.
"I'm very hopeful that this is just a minor hiccup."
Rangers return to the scene of their only league defeat of the season when they face Stirling Albion at Forthbank on Tuesday night.
Brian Allison struck for the Binos in a stunning 1-0 win back in October but since then the Ibrox men have gone on to open up a 22-point lead at the table summit.
That has now put them potentially within six wins of the title but McCoist insists his only focus is finally winning in Stirling.
He said: "That was the venue of our only defeat this season and I can obviously remember it well. It was a very disappointing performance. Certainly it was one of the blacker days of the season so far.
"So we will know what to expect. Even at Ibrox, I thought Stirling played well and made it difficult for us.
"But we are just concentrating on winning the league, not where or when we win it. I haven't even looked at when it could happen.
"Let's be quite frank about it. We have got ourselves in a great position to go on and win the title. Hopefully that is the case, and if it is, hopefully it is sooner rather than later."