Saturday's 3-0 defeat at the hands of Dundee United saw Rangers dumped out of the William Hill Scottish Cup, having already exited the Ramsdens Cup and the Scottish Communities League Cup.
"We've got everything to play for in terms of our main objective at the start of the season, which was to get promotion from the league," McCoist said.
The Light Blues are 19 points clear at the top of the Irn-Bru Third Division, meaning title success in the league is now just a matter of time. But, despite appearing to have little left to contest, McCoist says there is no chance he, or the club's supporters, will allow their campaign to simply fizzle out.
"The players will certainly know their responsibilities and duties are to go out and make sure it's not flat," he added.
"Our fans have been nothing short of fantastic and I'm sure they will not allow any flat atmosphere within any of the grounds we go to. It's my job to make sure the players are up for it - and they will be."
McCoist had claimed beforehand that United would be favourites to progress from the fifth round of the cup. But Rangers were left reeling when their hosts surged into the lead after just 16 seconds as Johnny Russell took advantage of poor defending. Jon Daly doubled the advantage with a free header, before Russell completed his double in the second half.
The win was United's first at home since August and allowed their new manager Jackie McNamara to enjoy a positive start.
Russell said: "I was delighted to get on the scoresheet myself but the most important thing was getting into the next round of the cup. It was a big game for Rangers but it was a massive game for us as well.
"They are still massive games when you play against Rangers and that victory feels just as good as it would if they were still in the SPL."
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- Dundee United