Translation:Sorry, we don't take credit cards.
If debit and credit cards are both covered by this term - and presumably charge cards as well, why isn't the more usual and generic 'sorry, we don't take cards' accepted? Reported. (Some retailers - both in shops and online in the UK will only accept debit card payments and refuse the use of credit cards)
No. Credit implies the provision of a loan (a line of credit). That is to say that you're borrowing money. "Credit card" is freely exchanged with "debit card" and doesn't specifically relate to borrowing money to pay for the transaction — just a method of generic card payment.
In English the sentence is not grammatically correct if you say "card" in the singular form. Other similar examples:
Sorry, no dogs are allowed in the store.
Please keep feet off the train seats.
No phone calls allowed.
No electronic devices allowed in the doctors office.
In English, if you were to say it in singular, it sounds like you are saying, specifically this one credit card is not accepted. However, the store rule is that (all) credit cards are not accepted. I hope this helps clarify the question.