Governing body of world football believe that they should have been told earlier about the claims over corruption, which included a vote in exchange for a knighthood
Former FA chairman Lord Triesman accused some members of Fifa's executive committee of wanting something in return if they were to vote in favour of England to be the hosts of the 2018 World Cup.
But England were knocked out in the first round of voting as Russia went on to win the right to host the tournament.
Triesman made accusations on Tuesday that there had been demands of money and a knighthood in exchange for voting in favour of the now failed 2018 bid.
But Valcke believes that this matter should have been brought to Fifa earlier, as he told reporters: "It could have been said before. If it was known, why did it not come to our attention? Why were we not informed?"
It had been thought that Fifa also failed to respond to a letter concerning allegations of bribery in the voting process that saw Qatar win the right to host the 2022 tournament.
"There was a letter and we did definitely reply," said Valcke. "But there has not been a single time, apart from what we got from a UK newspaper, where we got any evidence anything was wrong during the process.
"I'm not saying anyone is lying but if we had clear information that there was some kind of evidence we would have immediately asked for it."