The most high-profile case was a handball by France striker Thierry Henry in the build-up to the equalising goal against the Republic of Ireland in Paris which earned his country World Cup qualification in November.
And just hours after the IFAB's annual general meeting in Zurich, Birmingham's Liam Ridgewell had a headed goal disallowed in his side's 2-0 FA Cup quarter-final defeat at Portsmouth on Saturday - despite replays clearly showing the ball crossed the line before David James blocked it.
Valcke added: "Technology should not enter into the game, It was a clear statement made by the majority of the IFAB.
"Let's keep the game of football as it is."
IFAB is made up of representatives of the four British football associations, while Fifa hold four votes. Changes to the laws of the game must be approved by at least six votes.
Explaining his opposition to technology, Jonathan Ford, chief executive of the Football Association of Wales, said: "I was worried that you would end up with a stop-start situation where you review all decisions and I don't see that as part of the game."
Patrick Nelson, chief executive of the Irish FA, also backed Fifa's position.
"We very much appreciate the human side of the game, the debate, the controversy, that's why the board has taken this decision," he said.
IFAB, though, left open the possibility of using an extra official behind each goal - a system which has been trialled this season in the Europa League.
A special IFAB meeting will be held on May 17-18 to decide whether this system is used worldwide from next season.
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