Daniel Wass and Joakim Maehle struck in the opening 15 minutes for the hosts.
With right-backs Stephen O’Donnell and Nathan Patterson unable to make the trip for Covid-19 reasons, along with other players missing from Steve Clarke’s squad, Robertson started the match at right wing-back.
The home side, who reached the semi-finals of Euro 2020, sprung out the traps at the Parken Stadium and two goals in 15 minutes from Daniel Wass and Joakim Maehle had the Scots on the ropes.
It was not until half-time when Clarke re-jigged his side and put Robertson back over to the left-hand side that Scotland stabilised although there was no way back.
The Liverpool player said: “What we have showed is we have improved since three or four years ago, that potentially could have been three or four-nil but we dug in.
“Unfortunately we found ourselves two goals down, the second half you go out and try to get back in the game, you try to stamp your authority on the game, we have done that at times but I felt Denmark were always in control and that was the disappointing thing.
“We knew they would try to get off to a fast start in the first time back in front of this crowd after a fantastic Euros.
“Our aim was to quieten everything down and settle down into the game, we didn’t manage that and when you find yourself 2-0 down against a really good team, it is an uphill battle and we just didn’t have enough unfortunately.”