McBurnie caused a stir when footage emerged of him in conversation with some Sheffield United team-mates which appeared to be disparaging towards the Scotland squad set-up.
But manager Clarke is content with the explanation McBurnie provided in front of the rest of the players and backroom staff at the start of the week.
“It was completely clarified within the group,” said Clarke. “I did it in public, as it were, so everyone could hear the clarification.
“I could have just spoken to Oli inside, no problem, but it was better to do it outside on the training pitch. Clarified and clear - we have moved on and urge everyone else to move from it. It’s finished.”
The Leeds-born 23-year-old, who qualifies to play for Scotland through his Glaswegian father, has so far failed to score in seven appearances for the national team.
But with Hearts striker Steven Naismith likely to be denied the opportunity to win his 50th cap after being unable to train on Thursday as he nurses himself back to full fitness, McBurnie is favourite to play up front in the pivotal Group I fixture.
Clarke feels that McBurnie, now an English Premier League player after his £20 million summer move to Sheffield United from Swansea, can get the Tartan Army on his side and prove to be a real asset for Scotland going forward.
“I’m sure the supporters will get right behind the team,” added Clarke. “If Oli is part of that team, then the best thing he can do is go out there, play really well for his country, show everybody how committed he is”