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.
"Sean Dillon and Kris Boyd come together, Kris goes down and it's a penalty."