Roerslev featured in last night's 0-0 Nations League draw in Serbia.
Manchester United midfielder Eriksen said afterwards: "I just said that he is a good boy and he deserved to make his debut.
"He has worked hard for a long time, and when he first got going, he played a really nice game, the Danish captain told Bold, among others, after the game."
Roerslev also said: "It was fantastic to pull the national team jersey over my head for the first time. That debut was long overdue. I am happy and proud - especially when we also have a result. The icing on the cake would of course have been a win, but we got what we came for.
"We were a bit on our heels, and I was a bit shaky. I thought it might be a long fight. There were a lot of posts in the first 20 minutes where we struggled to deal with their two strikers, but we adjusted well and came after it well."
- Get breaking football news faster with the new Tribal Football app! Download now on iOS and Android to stay ahead of all the latest transfers and football updates. Download now: App Store, Google Play