In what was then still his first week in the job, Cotter took more of a back seat with the side before last weekend's 24-6 victory over the United States in Houston but the New Zealander has since taken a closer interest in Scotland's tactics and training for what is likely to be a fierce forward encounter.
"He had a small and limited input before the US game but this week has definitely been more hands-on, especially with the forwards," said Gray. "He wants us to play in a certain way and he's going through the drills in fine detail. He wants us constantly on the move, even in training. It's been tough but I am really enjoying it so far.
"He's made a big impression in his first few weeks that's for sure. The scrum was good against the USA, especially the front row, and that's what Vern was looking for."
Gray joined the Scotland party last week straight after playing for Castres against Toulon in the French Top 14 final in Paris. Having been on the Lions tour to Australia last year - he was the only Scot to figure in a Test - it has been a long and arduous season for the 24-year-old former Glasgow Warriors forward.
"I am looking forward to lying on a beach for a couple of weeks," said Gray. "It will be good just to shut down completely because it has been pretty full on for a year. I had the Lions tour last summer, the move to Castres and everything that has gone in between with Scotland.
"Being with Scotland has been great because it's a nice way to end what's been an incredible year for me. It's one I won't forget that's for sure. It's getting to the stage where the boys are perhaps not feeling their freshest. But it's a new coach and a new start for everyone and we have to ensure we all give it one last push."
Edinburgh lock Grant Gilchrist is expected to partner Gray in the second row against Canada, taking over - as he did in the course of the USA game - from Jim Hamilton, who suffered an ankle injury. Gilchrist backed up what his team-mate had to say about Cotter's increased involvement over the past few days.
"He did not want to bring too much in at once, being a new coach you can't throw everything at players but he is bringing in a few different things," said Gilchrist. "I hope we can take another step in the right direction this weekend."