The Rugby Park team, who failed at the first hurdle in their League Cup defence against Stenhousemuir last week, failed to really threat their hosts during the match at Dingwall.
The best chance for the Ayrshire outfit fell to McKenzie who was clean through on goal in the second half, but County keeper Michael Fraser pulled off a fantastic point-blank save.
And despite the miss, the 18-year-old believes a point is a good result, despite the views of his gaffer.
"A point up here is always good, but I'm a bit disappointed as I could have gotten all three points for the team," he said.
"It's tough coming up here. The pitch is quite tight and Ross County don't let you play, but in the first half we probably hit it long a few too many times. But in the second half I thought we got it down a lot more and created a few more chances.
"[Kenny Shiels] was pretty disappointed with the way we played, especially with me up front.
"You can't be pinging long balls all day because, as you can see, I'm not going to be winning headers against the two big guys.
"He went through us a wee bit. He wants to play football the right way and that's how everyone here wants to play, but sometimes you need to adjust.
"We're pleased. We had a wee scare with the goalkeeper early on, but that's the only chance they had. A point and a clean sheet is the way to go."