Credit cards are accepted throughout Croatia.  MasterCard and Visa,  American Express and Diners Club are widely accepted. 

ATM machines are also throughout the country. 

MasterCard and Visa are the preferred cards with American Express accepted at most hotels.  If you are planning to visit a small shop or restaurant, plan on paying in cash.
 
If you are renting a private apartment in Croatia you will not be able to pay by credit card.  You will need cash. 

If you book a room or a private apartment and wish to pay in advance, you will need to book through an online booking agency.  There you can pay by credit card.   Croatia is NOT fully serviced by Pay Pal so that option is not available when planning ahead.