Should You get distinctions in order to study in top universities in the US?

Should you get distinctions in your Masters in order to get into universities like Harvard, Stanford, Yale, Columbia, MIT, Berkeley, Caltech and so on for doing Doctoral degree. I received my bachelors degree with distinction but received my masters degree only with merit but not distinction. I did my masters at University of Edinburgh, UK. I took all hard courses and was unable to get very high scores. The ranking score there is that if you get between 60% and 69% you pass with merit and above 70% you pass with distinction. Only about 3-4 students in my course got above 70 and the first mark was 72%. Although all courses are electives and some courses are harder than the other.