The Danes beat Czech Republic 2-1 on Sunday (AEST) to progress to a fourth European championship semi-final – and their first since winning the tournament in 1992.
Hjulmand's side, whose tally of 11 goals in the competition trails only Spain, will face England at Wembley on Thursday (AEST) after Thomas Delaney and Kasper Dolberg saw them through in Baku.
Denmark – the first team to qualify from the group stage despite losing its first two games – has become the story of the tournament since Eriksen's cardiac arrest on the pitch in Copenhagen in its opener against Finland.
Eriksen has subsequently recovered and is in regular contact with his team-mates, who have gone from strength to strength, garnering a wave of support not just at home, but across the continent.
"I think the whole world of football understood that second, and the days after, the fundamental things in life and in football, the fundamental values of football came through right at that moment," Hjulmand said.
"There are so many other agendas in football, but we all remembered why we started to play football, what values football is based on and we had a reminder of this.
"I am still thinking of Christian every single day. He should have been here.
"We are happy that he survived, we carry him all the way to this match and all the way to Wembley. I think about him all of the time.
"We all understood maybe that the values of football came through – and maybe we are a symbol of it. I could not be more happy than that.
"We are just happy and proud we can maybe just remind ourselves why we love football and what football can do in the world."
Denmark's first-half display ultimately did the damage against Czech Republic, which dragged one back through Patrik Schick early in the second half.
Schick joined Cristiano Ronaldo at the top of the UEFA Euro 2020 scoring charts, but will not get the chance to add to his tally as Denmark held firm.
Delaney got things started for before Dolberg joined a host of Denmark legends on three goals at European championships, and the Borussia Dortmund midfielder added of Eriksen: "It is still something we are struggling with, but making him proud makes me happy."