The Constitution is "undemocratic" because our Founders understood that Democracy as a form of government always leads to tyranny.
As such, they designed a Federal Republic bound by fealty to the same Constitution, with the people's representatives acting under (small"D") democratic rules and procedures and elected by the popular votes of citizens.
Democracy as a form of government is glorified mob rule, wherein temporary majorities determine what are "rights" and who may possess them.
That always works out well.