We wouldn't say either of those.

If the meaning is that the words stuck in the mind - they will not be forgotten - then 'the simple words stuck in my mind' - the deeply part isn't really needed and doesn't sound all that natural. If the meaning is that the words held deep meaning for the listener, then 'the simple words struck a chord with me' - meaning they resonated, they connected with my own beliefs or made me feel deeply on the subject.