The Gers will look to take their second top-flight scalp of the season when Terry Butcher's side travel to Ibrox as they go head-to-head for a place in the Scottish Communities League Cup semi-finals.
McCoist's men have rarely hit top form in the Irn-Bru Third Division this season, but the Light Blues boss hopes they can pull off another cup shock.
He said: "The fans in many ways are looking at Rangers, for the first time ever, as underdogs – unless you're talking a big European game – and I think they're quite enjoying the fact that it's a chance to put one over on a team three leagues higher than us, who are going as well as probably any team in the SPL.
"Inverness have scored in every league game they've played in. The supporters are looking forward to the possibility of beating a team above us in the leagues.
"They look on it as an indicator to gauge where we are just now and hopefully where we can get back to."
While Rangers head into the Ibrox clash on top of the Third Division, and with their first away league victory of the season under their belt after their 2-0 win at Clyde on Sunday, Inverness have put together a solid run of form that has taken them to fifth in the SPL.
It has been an impressive campaign from the Highlanders thus far and McCoist knows his side will not have it all their own way as they look for a repeat of their 2-0 triumph over then SPL table-topping Motherwell in the previous round.
He said: "I have to tell you that we have been beaten by Inverness when we have been top of the SPL, so it's a tough, tough game.
"There's probably been as big a turnaround in personnel at Inverness as there has been anywhere else in the SPL.
"It's to Terry Butcher's massive credit – and the players – that they have performed as they have done this term.
"They looked a little bit slow to start but recent results would indicate that they're getting to know each other as well.
"I would settle for the same edge and same performance that the lads gave me the last time we played an SPL team, which came in the form of Motherwell.
"I think the fans will play a massive part as they have done for all our games this season, but I felt the atmosphere at the Motherwell game was almost like a European night.