Metro fines

I was recently in Copenhagen, I walked and biked everywhere except for one metro ride back to the airport.

My hotel very clearly told me I could pay by touching my credit card on the reader however that’s clearly not the case because an inspector gave me a fine. An exorbitant one at that… 750DKK. My taxi from the airport when I arrived was cheaper!

Is there any way to explain my genuine misunderstanding (which I don’t believe to be my fault, and besides that what major city doesn’t allow contactless credit card or Apple Pay to ride the metro!) to be let off the fine?

Some googling indicated that it’s not even a binding fine with no real consequences for non payment. Is this correct? I would like to live in Denmark one day and don’t want this silly ticket standing in the way.