Denmark were among the first teams to qualify for the tournament, decisively winning their group, and come into the event on the back of an impressive showing at the European Championship 18 months ago, where they reached the semi-finals.
“I think a lot of people hold us in high regard, given the way we played in the Euros and in the qualifiers,” he said on Thursday.
Damsgaard burst on the scene at the Euros, as he came into the side for the stricken Christian Eriksen, and is now a key part of their attack.
“I don’t think people are underestimating us. I don’t think we’re among the top teams but we’re a very good team and we can compete with anybody.
“Of course, we're not favourites, but I think nobody wants to meet us. I think among the big teams, nobody wants to go up against us.”
Denmark open their Group D campaign against Tunisia at the Education City Stadium in Al Rayyan on Tuesday, but have tougher tasks ahead against France and Australia.
“Tunisia is a team that we are better than, but we cannot underestimate them. We will have to have the right type of energy and don’t expect to just turn up and get the result.
“Hopefully we can kill the game early and not give them anything.”
Damsgaard said the change in mindset from playing for his English club just over a week ago to focusing on the World Cup, with virtually no preparation time, was not easy.
“It’s a first time for me so I’ve been taking it all in. It is not easy to make the switch but we have to do. We really don’t have a choice,” he added.
Danish Protests
Danish Football Association chief Jakob Jensen believes that Danish football's protest against Qatar's human rights record has delivered results, with conditions for migrant workers improving because of the international focus.
Denmark has been vocal in highlighting alleged abuse of workers' rights in Qatar ahead of their participation the World Cup, previously protesting with messages on their training kit and now blackening their team badge on their kit for the tournament.
The Danish players are also travelling without their families to the tournament in Qatar, which gets under way on Sunday.
"I think we've been able to make an impact on Qatar. It's been done by very many actors, not just the associations, but also organisations and international governments," Jensen, the chief executive of the football association, told Reuters.
"I think one has to be honest that there's been quite many improvements within Qatar legislation, and Amnesty International also reported that thousands of migrant workers actually have improved their conditions.
"But I think it's also fair to say we're still pushing for more."
Labour rights campaigners say Qatar has failed workers by falling short on reform commitments it made in order to become the first Arab country to host the tournament.
Qatar has rejected demands for a $440 million fund to compensate workers for labour rights abuses, including injuries and deaths, pointing to its own raft of reforms, such as higher minimum wages and an end to exit permits.
The International Labour Organisation has said reforms enacted in Qatar have improved the lives of hundreds of thousands of workers and are "significant for the region".
Jensen said Danish football would continue to use its appeal to take on other campaigns.
"I think that's going to happen. I do think that other issues are pushing their way on to the football agenda and we are trying to embrace them as much as we can.
"I believe in the power of football; I believe people can change the world," Jensen added.
