Their progress had captivated the crowds at Roland Garros where Nadal won 14 French Open singles crowns but their journey was ended in a 6-2, 6-4 quarter-final defeat.
Nadalcaraz, as they have become known since joining forces for the Paris Games, were given raucous support by a jam-packed Court Philippe Chatrier, at times the din sounding more like a football arena as the fans roared for the Spaniards.
When Krajicek served for the match and went break points down there was pandemonium with the umpire struggling to maintain order.
The American fourth seeds somehow kept their cool though and when Krajicek sent down an ace on match point it was met by almost silent disbelief - the umpire getting off her chair to confirm the ball had clipped the line.
Nadal began the Games by carrying the Olympic flame in the opening ceremony, but ends it without the third Olympic gold medal he craved on what could well be his last appearance on his beloved Parisian clay.
As he trudged off, fans snapped photos on their phones.
In truth Nadal and Alcaraz could have few complaints as they came up against a well-drilled partnership with Ram, a four-time Grand Slam men's doubles champion, superb throughout with razor-sharp net play.
In their two previous matches in Paris, Nadal and Alcaraz had ridden a wave of support, coming up with some inspired play to raise hopes that they could go all the way.
But this time, Alcaraz, who had reached the singles quarter-finals earlier, lacked his usual spark and served consecutive double faults to virtually hand the Americans the opening set.
There was no coming back this time and Alcaraz dropped serve to love at 3-3 - the Spaniards' frustration showing as they disputed a line call after a sizzling Ram winner.