If you are in the US and received good service, but left crappy or zero tips then yes, you definitely leave a negative impression of yourself. Nobody will understand why you left a bad tip or just think "oh, he's a foreigner, he doesn't understand." They will just think you stiffed them. Or they will perhaps think - "oh he's from country X - they must all be cheap assholes there. I hope I don't get any more tables with people from that country."
Would it not be the same if I visited your country and was rude or insulting regarding some very basic and obvious part of your culture?