Fifa president Sepp Blatter has condemned the “action of individuals” for bringing “shame and humiliation” on football.
But he said that although many held him “ultimately responsible” for the football community, he could “not monitor everyone all of the time”.
He was speaking at the opening of Fifa’s congress, a day after seven top officials were held in a US inquiry.
Mr Blatter is seeking re-election as president on Friday.
Speaking at the opening ceremony of the Fifa congress in Zurich, Mr Blatter said the events of the week had “cast a long shadow over football”.
He said: “The actions of individuals bring shame and humiliation on football and demand action and change from us all.
“We cannot allow the reputation of football to be dragged through the mud and it has to stop here, now.
“Many people hold me ultimately responsible for the global football community… I cannot monitor everyone all the time. If people want to do wrong they will also try to hide it.”
Mr Blatter said he hoped this would be a turning point for corruption.
“We must earn trust back through the decisions we make,” he said.
UK PM David Cameron urged Mr Blatter to resign but Russian President Vladimir Putin has backed him for a fifth term.
The head of European football’s governing body Uefa, Michel Platini, later said that if Mr Blatter were re-elected, Uefa might have to discuss its relations with Fifa.
Key sponsors have expressed concern over twin corruption investigations by both the US and Swiss authorities.