Rangers had made a mockery of their Third Division status with a dominant display in a 2-0 win against Motherwell in the previous round and hopes were high around Ibrox that the Glasgow giants could claim another Scottish Premier League scalp.
McCoist had said before the match that the tie offered his side an opportunity to show they could still compete with Scottish Premier League teams.
However, it proved to be a step too far for Rangers as Inverness progressed to the semi-finals of the competition for the first time in their history with a dominant display thanks to goals from Andrew Shinnie, Gary Warren and a Graeme Shinnie penalty.
It was a bitter blow to the Ibrox club, coming on the day the old club was liquidated at the Court of Session.
But despite showing obvious disappointment at his side's performance McCoist insisted his main priority was to get Rangers out of the Third Division. "It was an opportunity for us to compete against an SPL side again which we did do against Motherwell but I think the level and intensity that we played the game tonight was miles short of the intensity that we played the match against Motherwell," he said.
"In the second half we got what we deserved and so did Inverness.
"I am extremely aware of how far we have to travel. There is a thin line because it is very difficult but I will never make excuses.
"For example I won't make excuses for our second half performance and I won't make excuses for our slackness in defending at the three goals.
"But we have said for a number of weeks that we have a long, long way to go - tonight showed that.
"The league is without doubt the most important thing. We have to get out the league. Anything we do in the cups is a bonus. "That said after the disappointment of tonight, and it is a big disappointment, we have a very big game on Saturday against Alloa in the Scottish Cup."
Celtic progressed to the semi-finals on Tuesday following a 5-0 rout of St Johnstone at Parkhead with Kris Commons grabbing a hat-trick.
They will be joined in the draw by St Mirren, who defeated Aberdeen, and Hearts after they claimed a 5-4 penalty shoot-out win against Dundee United after the match at Tannadice had finished 1-1 following extra time.
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