The Light Blues crashed to an embarrassing defeat to Raith Rovers at Easter Road yesterday as John Baird netted the only goal of the game in the closing minutes of extra-time.
It capped a miserable afternoon for McCoist and his players, with the League One champions turning in an abject performance.
DJ told SportTimes: "I said last week Ally was in a no-win situation with regards to this game. He wouldn't have got much praise if he won because he was expected to and, if he got beaten, then he would get pelters.
"That is what is going to happen now over the next few days and he will know it is coming. There were a lot of angry fans at the end of the game, they made their feelings clear.
"The fans will slaughter the players and the manager, and there will be calls for Ally to go. He has to get on with the job. He is thick skinned.
"The players have got to up their game, too. The performances haven't been good for a while.
"You can't expect to just turn it on when you get to a cup final and too many weren't good enough yesterday."
"The game against Dundee United this week will pick everyone up, but they have got to get through this next couple of days because there will be plenty of flak coming their way."
After seeing his side fail to fire in their biggest game of the campaign to date, McCoist and his players must quickly regroup as they prepare for Saturday's Scottish Cup clash with Dundee United.
The Gers were strong favourites to lift the silverware in the Capital, but were far from their best as Rovers clinched a deserved win and DJ reckons the result will be a wake-up call to everyone at Ibrox.
He said: "It is a hard result to take. Rangers were expected to win and I don't know why people thought it would be easy for them.
"Raith are in a league above them and play good opposition every week.
"They are one of the best teams Rangers have played this season and they have fallen short.
"That tells (chief executive) Graham Wallace and the board that the team needs to be strengthened for next season.
"This squad might be favourites to go up, but there are no guarantees.
"There is a lot of work to be done and the performance and result yesterday just shows that again."