You are thinking about this question way too literally, Francine. =P Languages (fortunately or unfortunately) are not Math equations. You don't have a perfect, direct, word-by-word counterpart for everything in another language. Think about it: in Portuguese, we literally 'listen musics'; in English, one only 'listens TO SONGS' (how the hell do you 'ouve PARA canções', right?). In Portuguese, we 'need of' things; in English, why make it harder? Duh, you simply need them. =P
So, to say 'apesar de' in English, go with either 'despite' or 'in spite of'. There doesn't need to be an explanation; believe me, it's the easiest way. Over time, you'll get used to the new structure or term in question and your mind will think of it in the new language. To me, nowadays, saying 'despite of this' sounds as strange and ill-formed as saying 'apesar isto' in Portuguese, because my mind understands both constructions by their language's own logic.