actually yes you can but you have to add those speical characters by hand...
First you will need to findout if the character is within the 256 ascii characters and if not you will need to find out the unicode character of each one. the only two in your example that needed where the last two.
then do something like this:
str = "ÜÇ tas has hoaf"+String.fromCharCode(350)+" gÖtürüldü.";
regex = new RegExp('[^A-Z\\Ö\\Ç\\Ü\\I\\\\' + String.fromCharCode(350) + '\\\\' + String.fromCharCode(286) + ']', 'g');
alert(str.replace(regex, "").length); // 0
I used String.fromCharCode(350) for Ğ character because my browser didnt like me putting in unique characters, but if you are deriving it though a textbox you shouldn not need to worry about it. I aluse used \ characters more for a "just incase" browser compatability problem.