"In Brazil there are certain politicians who are against the World Cup, and the fact is that we've been through hell, essentially because in Brazil you have three political levels and there has been a change — there was an election and we're not necessarily talking with the same people (as before) — it was difficult to keep repeating the same message," Valcke said on Tuesday evening at a forum in Lausanne.
"It's not FIFA that is organizing the World Cup in Brazil, but Brazil, which is organizing the World Cup in 12 towns, Valcke said.
"We're supporting Brazil to ensure that it's a success because the whole of FIFA is based around the success of the World Cup," he said.
"If the World Cup is a failure then we, FIFA, are in trouble."
One of the main concerns has been consistent delays to the completion of stadiums.
FIFA had set a December deadline but this has been forced to be extended as several of the stadiums simply hadn't been completed.
"We should have received the stadiums in December, we'll receive them on May 15th (less than a month before the World Cup kicks off)," added the Frenchman, second in command at FIFA behind president Sepp Blatter.
"It's a little bit later than expected but we know how to adapt."
Valcke, however, warned 2018 World Cup hosts Russia that such leniency would not be repeated.
"If I can pass on just one official message, it is that Russia should not believe that delivering a stadium on May 15th is a point of reference," he said.
"I hope they will respect the timings."
However, Valcke admitted that certain works, for example in the town of Cuiaba, would not be finished by the time the tournament starts.
"I'm not saying everything will be finished," he said.
"But when it comes to the stadiums, after everything that's been said, having reduced our expectations and our needs, we'll have what is necessary to ensure that for the journalists, teams, fans and officials, there will be a World Cup that remains, I hope, especially if the drama of 1950 can be erased for Brazil, an exceptional memory."
Turning his attentions to Qatar in 2022, Valcke insisted the World Cup would be played in winter.
"The World Cup will be played in winter, I think everyone has said that and repeated it.
"Now we need to know when in winter it will be played and the executive committee will try to reply to that in March 2015."
He added that the tournament would be played in eight stadiums rather than the usual 12.
"I was the first person to speak with Qatar to say that there is no sense in having 12 or 10; eight is the right number of stadiums for the size of the country," he added.
FIFA rules state that an organizing country must have at least eight stadiums with at least one of those able to hold a minimum of 80,000 people.