The Euro 2020 semi-finalists fell at the first knockout hurdle at the Signal Iduna Park in Dortmund, where Kai Havertz and Jamal Musiala struck in the second half of a weather-affected match, which was halted for 25 minutes in the first half due to a thunderstorm.
Both sides had already had one goal disallowed before Havertz's penalty, as Germany's Nico Schlotterbeck headed in with just four minutes gone, but Joshua Kimmich was penalised for illegally blocking Andreas Skov Olsen.
Andersen then thought that he had propelled the Danes into the lead, only for Thomas Delaney to be caught marginally offside, before the Crystal Palace man was deemed to have committed a handball offence from David Raum's cross inside the box.
Andersen was in close proximity to the RB Leipzig left-back, but his arm was in an unnatural position, and Havertz calmly dispatched the spot kick after on-field referee Michael Oliver had taken a quick look at the pitchside monitor.
Hjulmand "tired" of "ridiculous" handball rules
Musiala then rubber-stamped Germany's place in the quarter-finals - where they will face either Spain or Georgia - with a breakaway goal, but the Scandinavians were left seething at the two controversial decisions that went against Andersen.
"It was decided by VAR decisions. I have a photo here, It was one centimetre (the offside). It doesn't make sense. This is not how we are supposed to be using VAR. It's one centimetre," Hjulmand told the media.
"Then there was the penalty. I'm so tired of the ridiculous handball rules. We can't require our defenders to be running with their hands by their sides. It's not natural. Joachim was running normally. He jumps up and he is hit from one metre.I rarely talk about these decisions. But they were decisive for this game. It's frustrating. Being in front 1-0 would have changed everything for our team."
Meanwhile, goalkeeper Schmeichel admitted that he still did not know what the rules were after 23 years as a professional, adding: "It's a mixture of disappointment, anger, rage, a bit of everything at the moment.
"This is football nowadays, I've played football 23 years and still don't know the rules yet. I'm not sure what a player is meant to do when he is running, and the ball is whacked at his hand from a yard away. I'm not sure football and common sense go together anymore."
Finally, Andersen - the guilty party for Havertz's spot kick - echoed his teammates' frustrations and conceded that he did not know what he could have done differently, adding: "It was crazy and not a penalty at all.
"I can't run around with my arms behind my back and play football. He's half a metre away from me and hits the ball on my hand, so I can't see what I could do to prevent it."
Are Denmark's frustrations justified?
Speaking on ITV following Germany's triumph, former referee Christina Unkel - who has provided unique analysis throughout the Euros - explained that proximity is no longer a factor in such penalty decisions, while highlighting Andersen's right arm still being outstretched as he rotated his body.
By that logic, Denmark can have few complaints about the awarding of the penalty, although one can sympathise with Andersen, Hjulmand and Schmeichel, especially as Oliver did not award the penalty in the first place.
However, the Delaney offside decision was correct in the laws of the game, and Denmark could also count themselves fortunate to see Schlotterbeck's header ruled out, as Kimmich's perceived foul on Skov Olsen was on the softer side.