The two sides were due to meet last weekend in a Division Three fixture, but Elgin were fined £25,000 after the match was called off due to 'a substantial oversale of tickets'.
McCoists insists his players have shrugged off the cancellation and are fully focused on continuing their cup run with a fourth round win at Ibrox.
"The weekend was a disappointment but we are over it and looking forward to the next challenge," he told the club website. "We now have to look ahead to the home game in the cup and against the same opposition."
Rangers claimed a 5-1 win over Elgin in the league earlier in the season, but McCoist is respectful of the threat posed by the visitors, who have matched his side's 29 goal tally in the league this season.
"They've been doing really well and I still think that Elgin are one of the better sides we have played this year even although the result at Ibrox would indicate otherwise," he said.
"We won 5-1 but they took an early lead and played fairly well in that game.
"When you look at the team at the moment I think they've scored the same amount of goals as ourselves albeit they have played a game more.
"But they certainly do have players in their team that can score goals and they do attack. So it's a cup tie we're looking forward to and we would obviously settle for the same result as the league game.
"I'm not sure we'll get that but I think Ross' team have certainly in recent weeks shown that they are a handful for anyone in the division."
The Gers could be boosted by the return of striker Francisco Sandaza who stepped up his recovery from a fractured cheekbone with a goalscoring display for the reserves on Tuesday.
Reserve team boss Tommy Wilson said: "I would think with the goal threat he carries and his experience he'll absolutely be in contention to be in the squad for the Elgin game.
"If you're looking at the bench for the match on Sunday and you're looking for a goal, he'd be an ideal man to bring on."