Son of former Scotland captain Darren Fletcher, the midfielder was among a group of youngsters used by Clarke to train alongside the squad over the past week.
The 19-year-old was then thrown on for his international debut in the second half of Saturday's 4-1 friendly win over Curacao.
Rangers' Connor Barron, Udinese's Lennon Miller and Andy Irving of Sparta Prague were the midfielders who had initially been placed on Clarke's reserve list.
But Fletcher has jumped ahead of them, despite having played just 17 minutes of senior football for United.
"I had to disappoint another three players this morning again, to tell them that they had missed out," said Clarke.
"I just felt Tyler came into the squad this week and showed up really well, did well in the game so that was the thinking behind that one.
"Obviously devastated for Billy and also really disappointed for Lennon, Andy Irving and Connor Barron."
Scotland fly out to the United States on Sunday to continue their World Cup preparations.
Clarke's men face Bolivia in a final warm-up friendly on June 6.
In their first World Cup for 28 years, Scotland will open their tournament with a clash against Haiti.