With the scores locked 2-2 at the end of extra-time, the qualifying tie went to penalties, with the Czechs eventually winning 3-1. Hojlund struck his effort against the bar.
The Manchester United loanee later told reporters: "I think I was playing one of my best country matches. I won almost all my duels, but unfortunately I didn't get to score.
"It's hard to assess where we stand. But I think we have delivered many good performances. However, we have stumbled right at the finish line a few times."
The Danes failed from the spot three times during the shootout.
"That's why it's also hard to put us among the best," Hojlund continued. "But I think we have a lot of quality. We have a skilled training staff. And I hope (coach) Brian Riemer continues in the post."