Southgate was already without centre-half Harry Maguire who was involved in a fracas on holiday in Greece before the squad gathered for the games.
The only positives for England from these two games was the fact that they return home unbeaten, having given debuts to four more players on Tuesday.
Defender Conor Coady of Wolverhampton Wanderers and Leeds United midfielder Kalvin Phillips made their debuts from the start, while Aston Villa's Jack Grealish and Arsenal's Ainsley Maitland-Niles came on for their first England appearances.
But it was the hosts who had the best chances in the League A Group 2 match with Inter Milan midfielder Christian Eriksen involved on both occasions.
Eriksen's clever turn in the 37th minute left his former Tottenham Hotspur team mate Eric Dier standing and set up Kasper Dolberg whose fierce shot to the near post was pushed wide by England goalkeeper Jordan Pickford.
Denmark keeper Kasper Schmeichel was also alert to deal with a Raheem Sterling shot from the edge of the box before Eriksen wasted a great chance in the 81st minute, firing over from a promising central position.
Simon Kjaer should have done better for Denmark with a free header in stoppage time while at the other end England captain Harry Kane rounded Schmeichel only to see his goal-bound effort cleared off the line by Mathias Jorgensen.
It would have been harsh on the Danes had Kane taken that chance and won a game which England, playing with five at the back, appeared to treat more like the friendlies of the past.
"I learned a lot. We tried a new system which we will get better at," said Southgate.
"We wanted to start with stability. We could have probably been a bit higher in terms of our attacking threat in the first half but we were in control," he added.
"In the second half we started to accelerate the game with the changes we made when we felt in control. [Substitutes] [Mason] Mount and Grealish in midfield made us more forward thinking."
Belgium, who thrashed visitors Iceland 5-1, lead the group with six points from two games with England on four, Denmark one and Iceland none.
England entered the match with some off-field drama after Manchester United striker Mason Greenwood and Manchester City youngster Phil Foden were axed from the Three Lions squad for breaching COVID-19 protocols to meet two women following Saturday's win at Iceland.