Fischer was outstanding for the Danes in their win over Armenia.
"I looked forward to the game for the whole week. It was great. It was one of my finest moments as a national team player," Fischer told Voetbal International.
"I know I can lose my place in the national team because I've been on the bench in my first four matches in England. But I am determined to fight my way into a starting place in Middlesbrough."
Boro will meet Crystal Palace this weekend.