The former Tottenham star required CPR before eventually regaining consciousness and being stretchered off the pitch and taken to a nearby hospital.
Eriksen's sentiments were relayed to the press by his national team manager Kasper Hjulmand, who revealed that the midfielder said: "Thank you, I won't give up. I feel better now - but I want to understand what's happened.
"I want to say thank you all for what you did for me."
The 29-year-old currently remains in hospital, where he is continuing his recovery in a stable condition.