Matt Ritchie’s eighth-minute goal was enough to give the Scots their second victory in six days, following last Thursday’s 1-0 win over Czech Republic in Prague, and ensure an encouraging start to Strachan’s preparations for the 2018 World Cup qualifying campaign later this year.
Scotland rode their luck during periods of the match, especially in the second half, but there were pleasing debuts for Celtic left-back Kieran Tierney and Hibs midfielder John McGinn.
“The better side were Denmark,” said Strachan. “We kept ourselves in it with a bit of grit and determination.
“If you look at the Danish players, they are all playing at a really good level, physically, and they are playing every week.
“Four or five of our guys don’t even get a game at their clubs right now.
“I wanted to make sure that no-one played in both of the games we’ve had this time. I wanted to send them back to their clubs feeling decent about themselves.
“We won two games of football and that’s great. But the other side of it, if you compare us physically with Denmark, is night and day. It was like a heavyweight against a middleweight.
“We need to learn from that. Our team spirit kept us in it, good defending and good goalkeeping.
“We had a couple of chances in the second half but they were basically the better side, because their players are at the top of their game.
“It was a gamble we took, although I didn’t expect Denmark to play as strong a team as they did for their second game of this international break.
“What did we learn? I’ve got a wide respect for the players I can pick from now. I’ve got a couple of young players coming through that we didn’t have a couple of months ago.
“I’ve learned players need to be playing regularly for their clubs. Only Alan Hutton has bucked that trend for us. Unless our football is tremendous with smaller players, we need to match them physically.
“Our passing wasn’t good tonight but that just comes from lack of fitness. You can’t pass the ball well unless you have top fitness levels.
“Kieran Tierney can be delighted with his debut. He’s been a breath of fresh air and now he knows what it’s all about.
“The process with John McGinn started when I worked with the under-21s a few months ago.
“His all-round demeanour, how he trained – I got him in there tonight.”
Strachan has now overseen 14 victories in his 27 games in charge of Scotland so far, experiencing eight defeats.
Scotland have two more challenge matches at the end of this season, against Italy in Malta on 29 May and Euro 2016 hosts France in Metz on 4 June, before their World Cup qualifying campaign begins with an away fixture against Malta in September.
“We will take the fittest, strongest and best to play in that next squad,” added Strachan.
“We will definitely get better. The players know that.
“There were four or five guys who have not played for a while, but they just give what they’ve got and they’re a great example of what you can do if you put your mind to it.”
For Denmark manager Age Hareide, it was his first defeat in the job after starting his reign with a 2-1 win over Iceland last Thursday night.
“We didn’t start well and Scotland took their early chance,” he said.
“But we were much better after that, especially in the second half, and had many chances.
“We should have got at least a draw, but it was a good test for us.”