The Spanish dream team lost 6-2, 6-4 to the US fourth seed, who progressed to the semi-finals in Paris.
Rafael Nadal and Carlos Alcaraz, dubbed “Nadalcaraz”, have been one of the main talking points at the Paris Games tennis tournament, wowing the crowds in their first two matches.
But they came unstuck in the last eight against doubles specialists Krajicek and Ram, who both have Grand Slam-winning pedigree.
Nadal was broken in the first game of the match on Court Philippe Chatrier and Alcaraz also lost serve as the US pair took the first set.
The Spaniards suffered another costly break in the seventh game of the second set, which ultimately proved decisive.
They battled tigerishly in the 10th game but failed to take advantage of three break points and Krajicek and Ram sealed victory on their second match point.
Nadal, a 14-time French Open champion, said after his painful defeat to Novak Djokovic in the singles competition in Paris that he would decide on his future after the Olympics.
The 38-year-old, immortalized in a statue at Roland Garros, has been plagued by injuries in recent years and is now 161st in the world.
Alcaraz still has a chance of winning a medal in the men’s singles competition he is through to the quarter-finals, where he will face US ninth seed Tommy Paul.