The Rangers boss was pleased by his team’s response to a disappointing cup exit seven days earlier as they ran out comfortable winners in the second half.
Now he wants his side to continue that level for the rest of the campaign and to build on the lead they have established at the top of the division.
He said: “In an ideal world that standard would be there for the rest of the season because they were certainly a lot brighter.
“They kept going in that second half and I was very pleased with the performance and result but also with the level of the goals.
“I’ve been saying for a few weeks now that we should be scoring more so today the level was good.
“It was just what the doctor ordered. I thought we had played quite well in the first half and I said to the boys at half time not to feel sorry for themselves.
“We hit the post and the keeper had a couple of wonder saves and they cleared one off the line so we felt we were doing ok.
“I felt that if we pushed our two central midfielders forward more in the second half then we would get the benefit, and thankfully that was the case.
“Within five minutes Kyle Hutton had a shot from the edge of the box and we might have scored from the rebound.
“Then of course Ian Black had a very calm and good finish from Barrie McKay’s delivery.”
McCoist was also delighted by the contribution of Andy Little, whose two goals took him to 18 for the season as he excelled in a striking role.
He added: “I think Andy fancies his chances, particularly through the middle. I thought out with his goals his performance was good as well.
“He led the line well and worked tirelessly. He was the main focal point and he won a lot of flick-ons which is an ugly side of the game that he did well.”