Andy Little fired a hat-trick and David Templeton also netted as Rangers extended their lead at the top of the Third Division to 19 points.
However, McCoist was unhappy with the second-half goals conceded as Ross Gray and Fraser McLaren gave Berwick brief hope of a comeback, and wants his side to be more ruthless in front of goal.
"There were three points, four goods goals and far more plusses," said McCoist.
"There were negatives too and I was really disappointed with the two goals we lost.
"Andy Little didn't defend the front post area well enough at the corner. We spoke about Berwick's corners and set-plays from that side.
"But it's difficult to criticise somebody who leaves with the match ball.
"There were positives and, at times, some of the football was good and we certainly had more of a cutting edge to our play today.
"But we could have and should have had more goals."
There was concern for Rangers when Chris Hegarty was forced out of the action after pulling up but McCoist does not expect a spell on the sidelines for the defender.
He said: "Hegarty's thigh went into spasm, which is a new one on me, but he seems absolutely fine.
"He was in seeing the doctor and we will get him in tomorrow morning to have a look as well."
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