The Glasgow clubs big-money stars could not get the job done yet again in the fourth tier making it two draws and a win from their three outings thus far and McCoist was not happy.
"I can't accept that and I won't accept that. I can't tell you how disappointed I am with the display," he said.
"It was absolutely miles short. No Rangers supporter or manager would expect that from the team. I've told the players it was unacceptable.
"There are a lot of aspects of the overall play that we are far from happy with.
"It was pretty clear to me there was a lack of confidence and that has to be a big concern."
Andy Little gave 'Gers the lead on the stroke of half-time with his fifth league goal of the season before Fraser McLaren hit back for Berwick just after the hour-mark.
Rangers now sit fourth on the Third Division table after three matches and next take on league leaders Elgin City at home on Sunday.