Roberts was an unused substitute in all three of Wales group stage games and the 22-year-old was again named on the bench for Saturday evening's last 16 tie in Amsterdam.
Caretaker boss Rob Page instead opted to start Cardiff City's Kieffer Moore upfront, flanked by Manchester United's Daniel James and Real Madrid star Gareth Bale.
Kasper Dolberg fired the Danes ahead in the 27th minute and Dolberg then bagged his and Denmark's second goal three minutes after the break.
Page finally changed his attacking line with 12 minutes left as both Roberts and Bournemouth's David Brooks came on for Moore and James.
Roberts looked to get quickly involved and produced some decent runs whilst attempting a total of five passes when he had the ball, three of which were accurate.
But the damage was done and the Danes bagged a third goal in the 88th minute through Joakim Maehle before Wales were reduced to ten men.
Liverpool's former Cardiff loanee Harry Wilson, who had been brought on for Luton Town's Joe Morrell on the hour mark, was shown a very harsh straight red card following a late tackle and Denmark made it 4-0 through Martin Braithwaite in stoppage time.
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Thank you Laura Collins