Tunisia's well-orchestrated rearguard defended in numbers and denied space to Denmark's attacking players, with a header off the post from Andreas Cornelius (29) the closest they came to scoring.
"Obviously, we are not satisfied with this, particularly with a big part of the first half and the way we started, but it can be okay if you score at the end of the match," Hjulmand told reporters.
"You put on the pressure that you want and try to score, but unfortunately we did not ... it's not a matter of the system, it's more our ability to hold on to the ball. We play too slowly, and at times that was the problem."
Hjulmand said the controversy over the 'OneLove' armband, which the team wanted to wear to highlight issues of diversity around the World Cup, was a difficult one, but the team decided not to after unspecified "threats that affect the sporting side" were made.
"This has not been designed for the World Cup - standing up for diversity, for every shade of people, that cannot and must not be a political statement. It isn't," he added.
"In Denmark we have this slogan, 'a part of something bigger', and right now I'm not sure if I'm a part of something that I like - I like the football, I love football. I love the diversity, I love all countries, I love different people.
"But I think it's important to change direction and hopefully a lot of young progressive people will enter a lot of governing bodies and make sure that we thrive and do something great," he said.
The Danes face world champions France, a side they beat twice in the recent Nations League campaign, in their next game on Saturday.
"We definitely had an aim of winning this one because we know of course a result in this game could have helped us, and now it could be complicated," Hjulmand said.
"But it's not over and we are still in it, it's one point each and now we have two very great games, and we're looking forward to France."
