McCoist's side blew their chances of recording a perfect season with a late collapse in their SPFL League One fixture at Ibrox yesterday.
They allowed Stranraer player Jamie Longworth to score an equaliser with the final kick of the ball in injury-time.
The disappointing result also brought to an end the Light Blues' record-breaking 20-game winning run in all competitions.
Rangers could actually consider themselves lucky to get a point from the game - they had only scored after being awarded a soft penalty.
And McCoist wants to see his side get back to winning ways when they take on second-placed Dunfermline at East End Park on Monday night.
He said: "It didn't happen for us at all. It wasn't us. We lost an appalling goal. I am quite upset about the goal that we lost.
"We have had a lot of praise for the run we have been on since the start of the season. But that was just not good enough.
"I am very hopeful that we will be able to perform a lot better than that when we take on Dunfermline in our next game on Monday night.
"I am not interested in the record. I am only interested in the level of our performance that the team produces and it wasn't good enough."
McCoist added: "I made two substitutions in the second half. I wanted to get a bit of life into the team, a bit of zest into our forward play.
"But it just didn't happen for us. It didn't happen for us at all against Stranraer. We had chances and hit the crossbar, but it was poor.
"We must do better than that and I would hope that our standard of play would be significantly higher when we play on Monday night."
Meanwhile, McCoist was pleased to see Andy Little, who broke his cheekbone and jaw against Dunfermline last month, make his competitive comeback.
He said: "That was a bonus. I am delighted to get Andy back. If I am honest with you, I thought he looked as if he had been out for a few weeks.
"But he will come on as a result of being involved in the game. It was good to get him on the park and back from a bad injury."
Stranraer boss Stephen Aitken said: "I thought we thoroughly deserved the point. For long spells we were in control of the game.
"If it wasn't for a wee dodgy penalty decision we might have got more. But if somebody had said they would have given me a point for a Christmas present, I would have bitten their hand off."