With right-sided defenders Stephen O’Donnell and Nathan Patterson unable to make the trip for Covid-19 reasons, Clarke sprung a surprise by moving his captain Andy Robertson to right wing-back with Kieran Tierney on the left.
Two goals in 15 minutes from Daniel Wass and Joakim Maehle had the Scots on the ropes and they struggled for the rest of the half.
Clarke brought on striker Lyndon Dykes for centre-back Scott McKenna, moved Ryan Fraser back to right wing-back, returned Robertson to his natural left-sided position with Tierney moving into the back three and Scotland looked more stable but by then it was too late.
The Scotland boss, who insisted his side are “still in the group” despite having only five points from 12, said: “It wasn’t an experiment, it was something that I was forced into doing in a way.
“I could have made other options but I felt that was the best way to start the game, experienced players on the pitch. I don’t think it was so much the personnel, it was the shape of the team.
“We allowed Denmark to pin us back, we made the pitch too long and the midfield couldn’t get close to the opposition midfield, we couldn’t get a handle on the game and I think it came more from team shape than personnel.
“It was a difficult first half for us, the Danish team started really well with good intensity, power and pace.
“We had to weather the storm and we couldn’t do that, we conceded two goals in quick succession which made it a long night for us.
“From 30 minutes in we started to get a foothold in the game but the game was a little bit beyond our reach at 2-0 down, it was always going to be a tough night after that.
“But I think we showed some signs towards the end of the half that we could get the ball down and we could play.
“We had to be braver on the ball under pressure and I think we were in the second half, the shape was better, we played five yards further up the pitch which allowed everyone to be more connected and it was a better second-half performance.”
Liverpool left-back Robertson insisted that he simply answered the call of duty.
He said: “The gaffer asked me and I said, ‘yes, no problem’. We were obviously short at right-back so the options were limited.
“The gaffer spoke to me and I didn’t hesitate and I will never hesitate, as long as I am playing for my country then I am happy.
“Of course I think you have seen in the second half I was a wee bit more comfortable on the left, that’s natural but on the right I gave it my best shot, I tried my best but unfortunately in the first half none of us were quite good enough.
“We took too long to settle into the game, me included, and we were all a bit too deep. It is what it is. Right wing-back was new to me but I will never shy away from it.”