A late winner from Portuguese striker Andre Silva means Dortmund is seven points adrift of Frankfurt and the UEFA Champions League qualification places.
"Realistically, it's going to be very difficult to finish in the top four, even if we get six or seven more wins," Hummels said after his side slumped to a 10th defeat of the season.
He said that missing the top four would be disastrous for Dortmund, which also faces a fight to hold on to coveted key players such as Erling Haaland in the next transfer window.
"Not qualifying for the [UEFA] Champions League would obviously be a sporting and financial catastrophe, and we are close to that now," Hummels said.
Frankfurt took the lead through a freakish own goal on 11 minutes, as Nico Schulz sent a looping header into his own net after a cross from Filip Kostic.
Hummels hooked the ball in at a corner to level the scores on the stroke of half-time, but the visitors restored the lead on the counter-attack in the dying minutes, Silva heading in from close range after another Kostic cross.
Frankfurt is now four points off third-place Wolfsburg, which beat Cologne 1-0 thanks to a second-half goal from Josip Brekalo.
Dortmund, meanwhile, is level on points with Bayer Leverkusen, which eased to a 2-1 win over bottom club Schalke in its first game under new coach Hannes Wolf.