The reputation of the game took a battering in last week's first legs, with Rangers slumping to a 2-1 defeat in Slovenia, Celtic being held to a goalless draw at home by Swiss side Sion and Hearts coming off worst of all three with a 5-0 thrashing by Tottenham.
McCoist is well aware of the importance of turning around that deficit at Ibrox and says Rangers are up for the challenge.
He said: "I can only speak for our own club and it is important. We all have a responsibility to do our best for the co-efficient and we will do that.
"This is an opportunity for us to do our bit and we know how difficult the task will be but it's not something we are shirking from. We feel we can do it and we will give it our best shot."
McCoist may have faith in his side's ability to book their place in the group stages but refused to look beyond the clash with the Slovenians.
He said: "Maribor showed enough in the second half to show us all that they're not a bad team.
"They can score goals and they've got some good players in their side.
"We did reasonably well in the first half and we had a far better performance on Sunday, which was a tough fixture for us against top-of-the-table Motherwell.
"If we can take our form from Sunday's game into this game, I would be happy. I would not be looking any further than this game."
Rangers head into the game boosted by a 3-0 win over Well in the Clydesdale Bank Premier League on Sunday.
With a number of first-team regulars unavailable, McCoist handed first SPL starts to Ross Perry and Jordan McMillan, while fellow youngster Gregg Wylde grabbed his first goal for the club.
And the Rangers boss insists he would have no qualms about giving youth a chance once again.
McCoist said: "I believe they did well enough to merit an opportunity against any team.
"You could say circumstances got them the chance, I wouldn't argue with that.
"But, at the same time, if you are given a chance and you take that chance, it would be a brave manager who wouldn't give youth that chance again.
"We are playing a team at home in what is a massive game for us but Sunday's game was a big game for us because we came off a poor result on Thursday night, we were going to a team at the top of the table, a team who hadn't lost a goal, and our young lads handled it well.
"That was very encouraging and, from that point of view, I wouldn't have any fears about playing them against anybody."
Meanwhile, Maribor goalkeeper Jasmin Handanovic admits he is not anticipating a quiet time at Ibrox.
He said: "I am expecting a busy night. There are games where there are hardly any attempts on goal and you still lose a match but I think this will be a busy night and a difficult game."