The Colombian striker, on as a substitute, saw his poorly-struck late penalty saved by visiting goalkeeper Nicolas Penneteau as the principality side ended 2013 in disappointing fashion and let slip the chance to go provisionally top of the French Ligue 1 table.
Instead, they remain two points adrift of leaders Paris Saint-Germain, who are already confirmed as autumn champions - the symbolic title taken by the side top of the table at the season's halfway stage - before hosting third-placed Lille on Sunday.
"We played well, created lots of chances, but when you don't have the luck it is difficult," Monaco coach Claudio Ranieri told French television. "Valenciennes played well on the counterattack, but I think luck was all that was missing for us. We will work hard when we come back from our holidays and try to forget this result."
On the fluffed spot-kick he said: "The goalkeeper read the kick well, but Falcao has confidence in himself."
Ranieri had left Falcao on the bench at kick-off as his side went looking for a sixth consecutive win. They had not conceded a goal in any of their last five outings but fell behind in bizarre fashion with half an hour played. Captain Eric Abidal bundled the ball into his own net after 'keeper Danijel Subasic had failed to cut out Arthur Masuaku's cross from the left.
The offside flag then denied Layvin Kurzawa an equaliser moments later, while Joao Moutinho struck the outside of a post from a free-kick, before Ranieri sent Falcao on for Emmanuel Riviere at the start of the second half.
However, Valenciennes went on to increase their lead just before the hour when veteran David Ducourtioux scored a rare goal at the end of a counterattack.
The hosts pushed forward desperately in the closing stages and won a penalty when Falcao was brought down in the box by Saliou Ciss. The former Atletico Madrid player's kick was saved, but James Rodriguez did head home to reduce the deficit soon after.
However, the same player had another effort disallowed for offside as Valenciennes held on for just their third win of the campaign and one which leaves them just two points away from safety before the rest of the weekend's games.