They tried on several occasions to pull the same scam on me in Athens near Syntagma Square. Once I actually went to the bar and had a beer, and they tried to charge me $100 or something like that. What I did was get up and say, "I'm leaving now and going straight to the tourist police." I left without paying and chalked it down to experience. The advantage I had was that I am Greek-American and gave them an earful in their own language.
Try to enjoy the rest of your trip and remember, soon you'll be back at home and that sleazy guy will still be in Istanbul, trying to make a living as a petty thief. Similar to something Oscar Wilde said to a woman who said he was drunk. His reply was, "I may be drunk, Madam, but you are ugly and I can rest easy in the knowledge that I will be sober in the morning!"