The former Argentina scrum-half had served as Sir Bill Beaumont's second-in-command at rugby union's global governing body before deciding to challenge for the chairmanship last month.
Pichot was eventually defeated 28-23 by the ex-England skipper at the election in early May, with French Rugby president Bernard Laporte serving as deputy chairman during Beaumont's second four-year term at the helm.
Pichot has now relinquished his role as the Argentine Rugby Union's (UAR) council representative, while he is also stepping down as president of Americas Rugby and giving up his seat on the board for the Rugby World Cup.
"The only reason I have been a part of World Rugby to this day, and which in turn is the same one that has moved me to run for president, is the conviction that World Rugby needs change," Pichot said in a statement.
"But my proposal, which I strongly believe in, has not been chosen, and that is why I choose to step aside.
"I cannot conceive of occupying a place just for the sake of occupying it."