Unsavoury songs were heard from a section of the travelling support during the Irn-Bru Third Division clash at Shielfield Park. Rangers responded during the match, which was broadcast live on ESPN, by releasing a statement condemning the actions of some supporters.
And, speaking after his side's 3-1 win, McCoist said he hoped the incident was a one-off, with the club having worked hard in the past to eradicate sectarian chanting at their games. He said: "If there was some unsavoury chanting, they've probably let themselves down - and they've let us all down a little bit."
He added: "I would be very hopeful it's an isolated incident and we can move on. Our fans have been fantastic home and away this season. I came off the park to be told the club have issued a statement. I back the club's statement 100 per cent."
Fans have largely been well behaved this season, after Rangers were demoted to the bottom tier of Scottish football, and McCoist added: "I think we've all come a long way in recent years. There's no doubt about that. We have to continue the good work that's been done before.
"You will get one or two setbacks, steps back to move forward again, but I'm hopeful it's no more than that."
It is understood the Ibrox club will assist any police inquiry into criminal acts and the club will ban those responsible from all Rangers matches.
A Rangers spokesman said: "The club is disappointed by certain outbursts of inappropriate singing by a section of the support at Berwick. Our fans have been excellent this season both home and away and we do not want to see this tarnished."
Superintendent Tim Smith, of Northumbria Police, said: "By and large, the fans were very well behaved, but there was a short outburst involving some sectarian chanting towards the start of the game. At the beginning of the game, we identified that some chanting had taken place and we have taken video evidence of that to do follow-up inquiries.
"In addition, two people have been arrested for that offence and are in custody. We have video evidence that will be investigated by officers from the FOCUS (Football Co-ordination Unit for Scotland) team from Strathclyde Police."
- Sports & Recreation