Platini announced on Wednesday he would stand in next year's election.
Bility told BBC Sport: "The world has asked for football and those who have managed football to be changed.
"Platini would not represent change, has been Fifa vice-president for eight years. He should not replace Sepp Blatter, it would be unacceptable."
Bility, Platini and former Brazil striker Zico are the three official candidates in the 26 February election to decide who takes over from Blatter, who is standing down following a corruption crisis.
The 48-year-old Bility is only the second African to try to become Fifa president but said "this is Africa's time" and insists he is determined to lead reform of world football's governing body.
That is something Bility believes Platini cannot do and he has questioned the former France international's record in office.
"When did Platini start being vocal about reform? Has he ever done that in the Fifa board room? Everything that we are trying to change today he has supported. Only now that he has declared his intention does he show some opposition to what has been before," Bility said.
"Platini has been the one saying Blatter is no good, Blatter should leave, but meanwhile he was in a board-room with Blatter. Every decision that we are all decrying today - there is no record to show that Platini decided otherwise.
"Platini's vote is right next to Blatter's vote. Why should we replace Blatter? If you bring in Platini there's no need to replace Blatter."
Prince Ali Bin al-Hussein, who may decide to stand in the election, has also voiced his concern over Platini's candidacy, saying "Fifa needs new, independent leadership, untainted by the practices of the past".
Bility is in "100% agreement with the Prince" and added that he wants to break Europe's stranglehold on football's top job.
"The records show that since the formation of Fifa there have been eight presidents. Seven have been Europeans. Are you telling me that the rest of us don't matter?
"We're in the 21st century and Europe has to understand that the rest of the world deserves to be head of this organisation. This is not the European Union, this is not Uefa - this is Fifa It is international. We need a change."
However, Platini appears to stand a good chance of winning the election after receiving indications of support from four continental confederations.
Asked if Platini might also receive backing from west African countries with historical links to France, Bility was adamant that would not happen.
"We are liberated people, we are Africans, not colonies of France. So nobody from French-speaking African countries are going to support Platini just on the basis they share a language," he said.
Bility is also eager to convert those supporting Platini to the Liberian's own cause.
"I call on European football federations not to vote for Platini, he's going to bring chaos into the organisation - he's going to bring more division, he's going to bring more problems. And Platini doesn't represent the change that we all want," he said.
"Fifa has to become fair and transparent. Platini's candidacy has served to re-energise my decision to run in the election and make sure I am the next president of Fifa."