The calls from the England international come after reports of offensive chants directed at Spurs teammate Emmanuel Adebayor during the North London derby against Arsenal at White Hart Lane on Sunday.
Parker says there is no place for abuse in the modern game and has called for authorities to act on anything similar in the future.
"It is probably the one sport that people can abuse other people and it seems half acceptable," he said.
"It is so wrong it is a joke.
"Just because you play for an opposing team doesn't give people the right to abuse you.
"I didn't hear it at the weekend but I have seen some of the stuff that has been written. If that was the case, the people who were involved need to be dealt with."