Wales, semi-finalists at Euro 2016 and second-placed qualifiers from Group A having taken four points from three games with Switzerland, Turkey and Italy, started brightly but faded badly after the opener and had substitute Harry Wilson sent off for a wild challenge on Maehle in the final few minutes.
Damsgaard's was his third in five internationals but his first in a competitive game.
Portugal proved too strong in the last four, however, the eventual champions running out 2-0 winners.
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Below the text is a list of the direct games.
They booked their place in the tournament with a 2-0 home win against Hungary in the last fixture.