With Christian Eriksen having also left, Dorgu and Chido Obi are left as the two Danes at the club.
He told Ekstra Bladet: "That's how it is in football. You never know when it's your turn to move on.
"We knew it would happen to Christian, but it was perhaps a bigger shock that Rasmus had to move on.
"I talked to him a lot during the process and could sense which way it was going. Hopefully, we will now see each other every time on the national team."
Dorgu also said, "I have been very happy to be team-mates with Christian and Rasmus.
"It was a big plus for me that they were at the club when I joined. That way it was easier to become part of the squad. But it was in no way decisive for my choice of Manchester United. I was thinking much more about the coach’s plans and ideas with me when I had to make the decision.
"I travelled alone to Italy when I was 17. I am also alone in Manchester and I am fine that way. You become incredibly strong mentally when you travel alone so early, because you have to make a lot of decisions. I am sure that mental strength has also helped me on the pitch."