Franklin and Grevers were just the latest big names to fall in Omaha, where Ryan Lochte had already failed to qualify to defend his 400m individual medley crown.
Franklin, whose four gold medals in London included the 100m and 200m backstroke, could manage only seventh place in the 100m back won by Olivia Smoliga in 59.02sec.
Kathleen Baker finished second in 59.29 to put herself on the road to Rio.
The only swimmer to finish behind Franklin was 33-year-old Natalie Coughlin, who won gold in the event in the 2004 and 2008 Games.
"Oh my gosh, it was a star-studded field," Smoliga said. "To have all those girls in there, and I know every single one of them, so it's so comforting to have them in the ready room."
"You know they're going to put up such a great race, such a great fight, and it was a fight," she added. "I'm just so happy with the outcome."
Franklin faced an uphill battle after posting the seventh-fastest semi-final time, and the 21-year-old couldn't produce a miracle from lane one.
Her time of 1:00.24 left her 1.22sec off the pace.
Less than half an hour earlier, she eased into the final of the 200m freestyle with the fourth-fastest time in the semifinals, which were led by the indomitable Katie Ledecky.
"I am feeling more pressure than I ever have before," Franklin admitted. "Right now, I need to make the team in whatever way that looks like."
Grevers, the men's 100m back gold medalist in 2012, came up just short in that event, finishing third in a scintillating final won by Ryan Murphy in 52.26sec.
David Plummer grabbed the second Rio berth in 52.28sec, with Grevers out in the cold in 52.76.
"My heart breaks for Matt," Murphy said. "He's been dominant in that event for so long."
But the 20-year-old who won relay gold at last year's world championships has high hopes of keeping the 100m back title in US hands.
"Hopefully, we have a good shot of going one-two," he said.
Townley Haas, 19, won the men's 200m free final in 1:45.66, just one one-hundredth of a second ahead of Conor Dwyer.
