Rangers' hopes of taking another step closer to the Scottish Cup final suffered a setback when they were pegged back by United despite fighting back from a goal down to take a 3-1 lead.
Andis Shala fired the visitors ahead before Kris Boyd netted twice from the penalty spot and Nacho Novo added to the scoreline for the holders.
McCoist insisted: "It's not all doom and gloom - far from it. We are still in the competition and we are the holders.
"We've got a great record in this cup and the good news is that we are still in it, albeit we face a really tough replay."
United boss Peter Houston said: "I was disappointed to lose what I thought were two soft penalties. I haven't seen them again and I might be wrong.
"But I thought the goalkeeper got his foot to the ball for the first one and, for the second one, I thought there could have been a foul on Danny Swanson as we are attacking Rangers, he felt his heels clipped and the ball dropped to Kevin Thomson and the rest is history.