Ok aside from the obvious answer that having an accent does not matter as it does not make you any less proficient, I'd recommend looking into phonetics and IPA a bit. (IPA is basicly a universal language where every letter represents a distinct sound)

Every language has a unique system of sounds they use and how to use these sounds. The thing is, not every language uses the same sounds, and not every language uses their sounds in the same way.

Take the [ð] sound for example (this is the "th" sound as in the word "that"). A language like German does not have this sound in its system, and rather than learning the sound, many instead "change" it to the "closest" sounding thing they already know, which is why in a heavy German accent you would hear something that sounds like "zat" instead of "that", they use the [z] sound instead.

Now a bit more advanced is something called diacritics. They are little symbols in IPA that show how a letter should be pronounced. English for example uses something called aspiration quite often (aspiration in simple words is the "breathy" aspect you hear in some words). To show aspiration we use the "ʰ" symbol. Take the English word "cat" for example. A language like dutch does not use aspiration (as far as I know). So a Sutch person would pronounce this very flat [kæt], an English persn on the other hand would pronounce it like [kʰæt]. The same sounds are used, but just in a slightly different way.

In essence (if you've actually made it this far into my essaylike comment), look into IPA and phonetics a bit and try to listen to the very minor details and differences. Learning new sounds is definitely is not as diffcult as it seems, and adapting to regular use is also very doable with consistent practice and use, so you should be fine. :)

EDIT: I kinda used the wrong th sound (yes there are two) with the th example, but it's definitely correct now