The Group B clash in Copenhagen was suspended shortly before half-time after Inter Milan midfielder Eriksen fell to the ground with no one around him.
Both sets of players decided to resume the game after more than 100 minutes away from the pitch, with Joel Pohjanpalo sealing victory for Finland in its first ever major tournament game shortly before the hour mark.
Speaking to the media after the game, an emotional Hjulmand was full of praise for the way his players rallied around Eriksen.
"It was a tough night," Hjulmand said. "We are all reminded what the most important thing in life is and that is to have valuable relations.
"We have a group of players I can't praise enough. I couldn't be prouder of these people who take such good care of each other at such a time where one of my very, very dear friends is suffering.
"All of our thoughts and prayers are with Christian and his family right now. Christian is one of our best players and he's an even better person, so all my thoughts and all my positive energy go out to Christian."
The players only agreed to finish the game once they had been assured Eriksen was in a comfortable condition, with Hjulmand revealing they were also given the option of resuming the match on Monday (AEST).
"There was no pressure from UEFA to play tonight," he explained. "We knew we had two options. The players couldn't imagine not being able to sleep tonight and then having to get on the bus and come in again tomorrow.
"Honestly, it was best to get it over with. Of course, you can't play a game with such feelings and what we tried to do was incredible."
Finland, which secured the win courtesy of its only effort on goal, has lost only one of its past eight competitive matches, picking up five victories and four clean sheets along the way.
While pleased to seal an important three points, boss Markku Kanerva acknowledged it was a challenging occasion for his players as well.
"It was a very emotional night for us," he said.
"First time in a major tournament and an opening game against Denmark in their home stadium. When we heard the national anthems, it was very emotional for us. And then what happened with Christian – a very dramatic and sad incident.
"And then finally, we get a good result from the game. Of course I am happy for that. Unbelievable. We are going to remember this for a long time for different reasons."