Inverness CT manager Terry Butcher says low crowds have caused him to question whether the Highland city deserves a team challenging for European football.
A crowd of 2,529 watched their 1-1 draw with Kilmarnock on Wednesday in poor weather conditions.
"I honestly don't know how much more we can do. We played some of the best football of the season," said Butcher.
"Does this city deserve a football team like we've got? I don't know."
Butcher is urging more fans to turn out, with his side currently sitting second in the Scottish Premier League table.
Inverness have the second-lowest average attendance in the SPL at 4,017 - higher only than St Johnstone and lower than fellow Highlanders, Ross County.
"I know it's difficult weather, but I don't know how much more we can do," said Butcher.
"We cannot do any more: second in the table, could have gone three points clear of our nearest rivals for second place with eight games to go before the split."
However, Kilmarnock manager Kenny Shiels was adamant that crowds at Scottish matches were as good as could be reasonably expected.
"If you look at the population of Scotland, our game is a very well supported product," he said.
"Two and a half-thousand on a Wednesday night with Champions League on the television - that's a very good crowd. Did you see the snow? You wouldn't believe it.
"We are doing great in Scotland. What's the crowds in Finland? There's five million population there. Go look up their crowds. They are not great.
Shiels also asserted that changes beyond the confines of football were the reason for a general decline in attendances.
"You have to look at the societal changes that have gone on. In days gone by a cup of tea was a novelty. Now we are in the computer age. That is why the crowds have gone down."