McBurnie netted shortly after the hour mark for Scotland to secured Ricky Sbragia's side a 1-1 draw with Croatia but Austria's 2-1 victory over Italy at the same time saw them progress at the Scot's expense.
McBurnie's starting appearance on Tuesday against the Croatians was his third in recent days for the Scottish Under 19s after also playing against Austria and Italy in their Elite Round qualifying group.
The 18 year-old, who made his debut for Scotland's Under 19s against Holland back in November, is currently on loan at Vanarama Conference side Chester FC.