First of all, you want to be understood, and for this there's a minimum pronunciation correctness that you must achieve. Some people decide to stop when they have reached that level, and speak all their life with strong accents (do you know any French ?).

You should always try to get a perfect pronunciation, especially the intonation, the music of the word. This as a politeness to your listeners and because it's better to do things well. Of course, perfect pronunciation is not easy to achieve, and you should not be ashamed if people recognize your accent. But it would be shameful to rest lazily on the rythm and the phonemes of your mother tongue when you speak in another one.