The midfielder struck a wonderful effort from 30 yards after Three Lions midfielder Mason Mount had conceded a foul outside the penalty area.
The ball flew over the England wall and beyond goalkeeper Jordan Pickford.
The Everton shot-stopper received some criticism by commentators and pundits for not stopping the effort, which went in slightly left-of-centre of the goal.
But Denmark appeared to breach FIFA’s rule book in the build up to Damsgaard stepping up.
Bukayo Saka’s cross was turned into his own net by Denmark defender Simon Kjaer.
Former England defender and ITV pundit Gary Neville was unhappy with Pickford for his role in Damsgaard’s goal.
The ex-Manchester United right-back said he feared that the Sampdoria star would score as soon as he stepped up to take the free kick.
“Most definitely [Pickford should have done better],” Neville said.
“We feared the worst when they lined up.
“The goal was coming, Denmark were getting through us far too easily, it’s a long way out and I always think if the ball goes in the corner there’s no problem.
“The ball goes in the centre of the net, and the goalkeeper has to do better.
“His big problem is that ultimately he’s blocked, he doesn’t see it until late, then he goes late himself.
“But he has to get in a position where he can go earlier, it’s right above him and he’ll be really disappointed.”