St Mirren and Ross County both opted against the introduction of a new 12-12-18 league system, with a majority of 11-1 required to send it to the Scottish Football League.
The proposed structure would have seen the top two leagues split into three after 22 matches, resulting in increased revenue and a more even spread of finances.
"This is going to have major implications for Scottish football - it's going to potentially seriously damage the game in the long term. I'm very angry because I think today we have let down Scottish football," said Milne.
"St Mirren Football Club have really got to pose themselves the question: why are they prepared to put the rest of Scottish football in jeopardy just because of their own selfish interests?
"This is a massive opportunity that has been blown, particularly on the whims of an individual. In that room, we've got to be in there with the interests of our club but we've got a wider responsibility for the SPL as an organisation and also wider Scottish football. None of that was displayed by [St Mirren chairman] Stewart Gilmour and St Mirren Football Club."
Rangers have defended St Mirren and Ross County over their decision.