"The point is that the whole nation is in the midst of a cold snap right now and there was no indication that the weather was going to clear.
"It's all very well having a cover over the pitch but when the temperature drops to the level it did last night it simply freezes the moisture underneath the covers.
Bain added that despite asking for a decision on the match as early as Thursday, given the forecast of freezing temperatures, he was told that the earliest an inspection could take place was 24 hours prior to kick-off.
"We have made the point to the football authorities on numerous occasions that our fans come from far and wide, especially those who go to away matches," he said.
"The very reason we wrote to the SFA on Thursday was to avoid this exact scenario.
"We are really disappointed by all of this and we feel sorry for those fans who had already set out on their journeys only to learn that the match was off."
The postponement also means the draw for the quarter-finals, which was due to take place after Sunday's match, has been rescheduled for 1715 GMT on Monday at Hampden Park.
The match has been rearranged for Wednesday 18 February.
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