The holders were sent crashing out of the Scottish Communities League Cup by Irn-Bru First Division side Falkirk midweek.
But they hit back in style by taking all three points at East End Park on Saturday to strengthen their grasp on top spot in the Scottish Premier League.
McCoist said: "It was just what the doctor ordered. The performance was as good as the result.
"We got a great reaction and I felt that we would get a good reaction.
"That's not to say that I wasn't worried about the game, you are always worried about the game, but I wasn't worried about getting a reaction.
"The reaction to Wednesday was very, very pleasing.
"That game is gone now, it's fish and chip paper. It was a real disappointment but it would be a bigger disappointment not to learn a lesson from it.
"That's all we can ask for because there is nothing we can do about that result now."
Steven Naismith grabbed a double and Carlos Bocanegra and Maurice Edu were also on the scoresheet.
But McCoist felt his top performer on the day was stand-in skipper Steven Davis.
He said: "You don't like singling out individuals but it would be wrong of me not to say what a performance that was.
"It was absolutely top class, it was a real captain's performance.
"I thought he was out of this world."
Television cameras showed Naismith apparently catch Austin McCann on the face with his elbow, but McCoist did not believe there would have been any malice involved.
He said: "I didn't see it. I saw Austin McCann go down. I thought Naisy won the header.
"He's certainly not that kind of boy. He's very, very competitive. As I say, I didn't see the incident."
Pars boss Jim McIntyre was also unaware of the incident and admitted there were no complaints from his player.
He said: "He's not mentioned it. I didn't know anything about it."
Reflecting on the defeat, McIntyre added: "The performance was abysmal and the result matched that.
"I felt after the first goal that too many went into their shell. It just went from bad to worse.
"But these are not the games we will be judged on at the end of the season. The games we will be judged on are against the teams at our own level."
Source: Team Talk
Source: Team Talk