Andy Little claimed a hat-trick and David Templeton was also on the scoresheet as the Light Blues stretched their lead at the top of the Irn-Bru Third Division to 19 points. However, the Rangers boss was unhappy with the second half goals netted by Ross Gray and Fraser McLaren which briefly raised Berwick's hopes of a comeback.
McCoist said: "There were three points, four goods goals and far more plusses. There were negatives too and I was really disappointed with the two goals we lost."
The Gers boss added: "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."
Elgin's late fightback earned them a share of the points last week and McCoist was not surprised to see Berwick claw themselves back into this game.
He added: "I am believing everything that's happening at the moment. As disappointed as I was when it went 3-2, I could believe it. There is not a lot shocking us at the moment. Believe me, it was believable."
McCoist had some sympathy for Francisco Sandaza, who was involved in much of the action but could not find the back of the net. The Spanish striker is seeking a return to form after a lengthy spell out of action with a fractured cheekbone and looked desperate to add to his one goal for Rangers so far.
McCoist said: "He did everything apart from score. I felt for him in terms of not getting a goal but that was the only thing lacking from his overall performance.
"The argument is that a centre-forward should be scoring goals. But, that said, his contribution was very valuable to the team. You can see him becoming just like his old self."