An own goal from Simon Kjaer cancelled out Mikkel Damsgaard's opener for Denmark, and after the game had finished 1-1 in normal time, England were awarded a penalty in extra time. Harry Kane's spot-kick was saved by Kasper Schmeichel, but the England striker scored from the rebound.
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"We're very, very disappointed, and it's hard for me to talk about," Hjulmand said after Wednesday's loss at Wembley. "Maybe it will [be] easier for me to say how I feel in a few days."
Raheem Sterling drew the penalty when the Manchester City forward wriggled into the area down the right, cut inside and fell under the challenge of Mathias Jensen. The contact looked minimal, and a video review was needed. After a brief wait that must have felt longer to England's fans, the decision stood.
"We're just very disappointed that we were so close to the final," Hjulmand said. "We're disappointed it was decided that way. ... It was a penalty that shouldn't have been a penalty, and that annoys me right now. We're disappointed, we're very disappointed.
"It's one thing to lose a game, that happens, but losing this way is just a disappointment, because these guys have fought a lot. It's bitter; I think we have to digest this before we can describe these feelings, but it's a bitter way to leave a tournament."
The build-up to the penalty decision also saw an extra ball make its way onto the pitch near the touchline. Play continued despite the extra ball, with Sterling drawing the foul seconds later.
Asked about the foul, Sterling said he felt the referee made the right call.
"I went into the box, he stuck his right leg out and he touched my leg so it was a penalty," Sterling added.
On the extra ball and the penalty decision, England manager Gareth Southgate said: "I saw the [extra] ball on the pitch so I wasn't sure how that would be dealt with. But, I saw a game in England where that happened and the goal wasn't disallowed. I haven't really seen the penalty situation, but a lot of people have asked me the same question [if it was harsh on Denmark]."
On seeing his initial attempt from the spot blocked, Kane reacted quickly to put it into the net from 6 yards out.
"I was fortunate to have it bounce back,'' Kane said. "That's football -- sometimes it falls your way.''
Despite the own goal and the loss, Denmark captain Kjaer left the pitch with his head held high after an extraordinary campaign by Denmark. It has been an emotional roller-coaster for the Danes, which started when midfielder Christian Eriksen suffered a heart attack in their group-stage match against Finland.
"It's been a great journey, and I'm sorry it's over now," Kjaer told broadcaster DR. "I think when we get some distance, there are things that will come up. It has been hard to take in, but a great journey. I'm sorry we did not make it all the way to the final."
Hjulmand thanked the people of Denmark once again for their support.
"I'm grateful for Denmark, the entire nation," he said. "We needed the support, the empathy when that happened with Christian. We've been receiving a lot of love, a lot of support and that was amazing to feel.
"Our future is full of hope and belief, these guys are outstanding and the whole nation can be proud. Keep giving them the love and the respect they deserve. ... We can be incredibly proud."
Information from Reuters was used in this report.