"We are working in conditions where the cement is not even dry," Valcke told reporters as Tuesday's 100-days-to-kickoff milestone approaches.
"We still have to install all the IT solutions for the media. Without IT and without the telecommunications in place in the stadium you will say we are the worst organisers and it was the worst event.
"But to install the IT in a stadium, it needs at least 90 days and we have to work for all the people who have an interest, our commercial partners, our media partners, hospitality......
"The ball starts rolling on June 12 until July 13 and I think things will work well then but it is also true that whenever you receive something late, it becomes a challenge to make it ready in time," Valcke added.
"I am not a World Cup specialist but I will say this has not been easy for sure," he told reporters gathered after a meeting of the annual International Football Association Board, the game's law-making meeting.
"We are almost at 100 days before the first game starts in a stadium in Sao Paulo which is still not ready and won't be ready until May 15.
"And as you know another two stadiums (in Curitiba and Manaus) are quite late."
Two years ago this weekend Valcke delivered his famous "Brazil needs a kick up the backside" line which incensed the local organizing committee, but certainly had something of the desired impact.
Asked if the Brazilians now needed another kick up the backside, Valcke deflected the question.
"Ask me that when the World Cup is over," he replied.
"We have already had to put things in place and it is very last minute work, but it will work at the end. It will work, and you will have what you expect and the teams will have the best.
"For sure, the stadiums are beautiful but now it is a challenge for the organisers. And that is not a criticism. It is just a challenge. We have to find the solutions."
- Sports & Recreation