Yes, you must let the credit card companies and your bank know you are going abroad. I used my debit card towards the end of my holiday one year a couple of times and when I got home I couldn't use it and on ringing the bank was told it was as there was activity abroad and in the future to let them know. I always do now even if I do not think I will use them.
Have used credit cards for the past 6 years in numerous restaurants including Set steakhouse, Romance, Harry's, Holiday, Cupid's, Lemon Tree, Majestic, Florida,and new for this year Turkish Delight and Blue Fox, without any problems. I don't leave my card out of my sight at home or on holiday.