He was delighted with the goals and some individual performances and also a clean sheet.
However, the down side was an injury to Ian Black who has a knee problem which will be assessed fully tomorrow. Dean Shiels, Kevin Kyle and Kal Naismith got the goals as Elgin were beaten 3-0.
McCoist said: “I’m delighted. The main objective is to get through to the next round and we did that but I thought our goals were well executed and there some good individual performances in the team too.
“One of the most pleasing aspects was keeping a clean sheet. We switched off a couple of times but Neil Alexander made a great save and Darren Cole blocked one on the line too.
“I said the lads before that Elgin score goals because they have good front players so it was an awkward tie for us and therefore I’m pleased we came through it.
“I thought McKay’s performance was as consistent throughout a match as he has been. In other games he has shown flashes of good play and intelligence but he did it throughout the game today.
“One of the pleasant problems we have when players are coming back is picking our bench and we felt Kal deserved a place on it after scoring in the East Stirling game and looking sharp in the Reserves.
“So I was delighted that he came on and got his goal today. He took it well.”
The 5th round draw takes place tomorrow and McCoist doesn’t really mind who Rangers face. He said: “I don’t see any reason why we can’t do well against an SPL side if we are drawn against one.
“We performed well against Motherwell when we played them in the League Cup. I wouldn’t start screaming from the roof tops that we are ready for anything by an SPL team wouldn’t scare us.”
The one negative was the injury to Black, McCoist said: “He is struggling a little bit. He over-stretched after about 25 minutes and we had a look at him at half-time but Ian thought he could continue.
“We will assess him tomorrow but at this stage it might be a couple of weeks. It’s the back of the knee but hopefully it won’t be too serious.”