burak, you definitely have an accent, but then, I don't see anything wrong with it (?)
Accents are part of who we are... Although... I'm going to ramble...
I was just talking to someone the other day about my mom (she's Filipino) - to me, she's got this very thick accent (I was born in D.C. back in 69, so I have, um, an "American accent"(?))... anyway, when she goes to visit the Phillipines, those folks over there thinks she has an American accent even though she is speaking Togalog, which is one of the dialects over there. What does this mean? Nuttin'... Just thought it was interesting.
If I were to have a Filipino accent, my F's would be P's (typically). For example, "Everybotty was Kung Poo Pighting. Them cats were Past as Lighting." Again, this means nothing, but I never really get to type about this stuff.
I think accents add character relative to whomever is listening. That means a little something.
(sidenote: I read with an English accent, like Shakespeare)