"I am devastated for Billy because he has been an integral part of our World Cup qualifying campaign," said Clarke.
The national team manager emphasized the difficult timing of the setback but backed the midfielder to recover for future international tournaments.
"The timing of this injury is so, so cruel and we all feel for him," said Clarke.
The head coach added that the entire squad holds Gilmour in high regard as both a footballer and a teammate.
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"He knows what we all think of him as a footballer and a person and while no words will give him any comfort, I am certain Billy will have many major tournaments ahead of him in the future," said Clarke.
Clarke later shared his impressions of Fletcher's second-half performance during his debut at Hampden Park.
"Everybody was impressed - the players were impressed, the coaching staff were impressed, I had no doubts," said Clarke.
The manager explained his decision-making process regarding the timing of Fletcher's introduction to the match.
"I actually thought about putting him on as Billy came off but I just thought I'd have a little look, see how the game panned out before introducing him at half-time," said Clarke.
Norwich City midfielder Kenny McLean, who previously played alongside the teenager's father, Darren Fletcher, shared his evaluation of the young player's potential.
"I said to the lads after his first session, I could see something special in him, so I was glad that he got on," said McLean.
McLean compared the debutant's attributes to those of his father, the former Scotland captain who earned 80 caps between 2003 and 2017.
"In my first session with Scotland, Darren stood out a mile. Fortunately for us, his son is pretty similar.
There's a lot of potential, it's about using him the right way," said McLean.
The Scotland team travels to Florida on Sunday, May 31, 2026, ahead of a final warm-up fixture against Bolivia in New Jersey on Saturday, June 6, 2026.
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Scotland will compete in Group C against Haiti, Morocco, and Brazil, marking their first World Cup finals appearance since 1998.