When Germany’s last-16 game with Denmark on Saturday was disrupted by a huge storm, many home fans shielded themselves from the heavy rain and hail under coloured boards they had earlier held up to form their national flag.

It may have been futile and they ultimately got drenched, but not even that could dampen their celebratory mood at full-time in Dortmund, as the Euro 2024 hosts sealed a 2-0 win to reach the quarter-finals.

The final whistle was greeted by a huge rendition of the 1983 song Major Tom, which has developed into the host nation’s unofficial anthem for this tournament, as the sense of belief among home fans that their side can go all the way grows with every game.

But fortune also plays a part in tournament football and Germany arguably had that in this win as two decisions left the Danish camp furious.

The first came in the second half when, with the score goalless, Joachim Andersen saw his strike ruled out after Thomas Delaney was ruled inches offside in the build-up according to the semi-automated offside technology.

Then, Andersen’s misery was compounded when Germany were awarded a penalty moments later after David Raum’s cross touched his outstretched arm.

It left Denmark’s coach Kasper Hjulmand fuming in the post-match news conference.

“It was decided by two VAR decisions,” he said. “16 seconds of a decisive moment.

“I rarely talk about these decisions but it was very decisive for this game. It is frustrating. It is frustrating for our team.”

Denmark did not win a game in the group stage, so an exit at this stage of the tournament was not unexpected.

But that will not make the decisions that went against them on Saturday night any easier to take.

They thought they had gone in front just after half-time when Andersen scored, but the effort was eventually ruled out following a VAR check which showed Delaney was just offside before setting up the goal.

When play restarted, Germany immediately attacked and Raum’s cross brushed off the arm of Crystal Palace defender Andersen in the Danish box, leading to another VAR check and the award of the penalty which Kai Havertz converted.

In the post-match news conference, Hjulmand pointed to photographic evidence on his mobile phone that highlighted just how marginal the offside goal that denied them the opener was.

“I have a picture of one centimetre offside call, it is not possible,” he said. “You cannot call a one-centimetre call.”

For the handball decision, given 16 seconds after Anderson’s goal had been ruled out, Hjulmand added: “We have been told our defenders should not run around with their hands behind their back.

“It was 16 seconds that were the decisive moment in the match. When VAR is used like that it is just ridiculous.”

Pundits analysing the game afterwards agreed.

Former Premier League footballer Dion Dublin told BBC Sport: “To rule goals out for that, what are you supposed to do and the handball is even worse.”

Ex-Wales captain Ashley Williams said on the handball: “You have to do the arms behind the back, which is absolutely ridiculous because it hinders the art of defending.”

While former Manchester United skipper Roy Keane, told ITV: “I’m always critical of defenders coming out defending with their hands behind their back, but I see it. I feel for defenders.

“That’s not the game we grew up loving, these types of decisions. People wouldn’t be waking up tomorrow saying ‘why is that not a penalty?’

“I’m OK with the offside. Offside is offside. I go back to the handball and I just can’t see it as a penalty.”

New technology is being used at the Euros which allows officials to see clearly if the ball has brushed the arm of a player, similar to the snickometer used in cricket.

Mixed results in the build-up to this tournament had provided a sense that not many Germany fans believed their side would be capable of challenging for a first European Championship win since 1996.

But the 5-1 victory against Scotland in their opening game was the ideal start they needed.

They possess exciting attacking talent in Jamal Musiala, Florian Wirtz, and Havertz, have experience in the likes of Toni Kroos and a super sub in Niclas Fullkrug, who has scored two goals in four games from off the bench.

With 10 goals in their four games so far, they are the highest scorers at Euro 2024, but manager Julian Nagelsmann believes they can still get better.

“There is always room to grow,” he said.

“Talk about the first 20 minutes in this game and it was very good, very happy with that.

“But we could speed up our game in ball possession. If we do like we did in the first 20 minutes it is really, really tough to beat us.”

“This game was an important win and it will give the Germans real belief that they can go on and run anybody close,” former Premier League striker Chris Sutton, commentating on the game for BBC Radio 5 live added.