The problem called θ

What is the thing that most likely gives away your native language is not English? Most of my

fellow German speakers will probably agree it's the th (θ) sound. After studying English for a long time now I feel pretty confident speaking it but this certain sound still gives me trouble (I was just told yesterday how cute it is that I Say f whenever I'm supposed to say th)

I have to admit I'm not trying hard pronouncing this sound correctly, but frankly I don’t hear that much of a difference between th and f. I guess this comes from my native language not knowing this sound and therefore my hearing not being sensitive to it. It's the same when my Croatian teacher tells me there's a difference between č and ć as well as between š and ž. They sure are there but I have trouble hearing them especially when in a word or sentence.

There also wasn't a big focus on pronouncing that certain sound correctly in school. We were told if we cant manage the th we should say f instead, and never z like a lot of people here do which lead some kind of cliche. If we are honest what will an American do trying to mimic a German accent? Exactly they will put a z wherever a th is needed.

“Excuse me can you give me ze water? I'm zirsty. Zänk you very much.”

But well since German is one of the few Germanic languages without that sound I guess the only thing we can do is practice practice practice if we don't wanna sound like that.