The Chivas, who lost 2-1 at Tigres UANL and had three players sent off on Saturday, are all but mathematically out of the Clausura quarter-finals with two matches left in the league phase of the championship. They sit 14th with 15 points from 15 matches.
The top eight in the standings go into the knockout phase with Apertura champions Tigres, Santos Laguna, Morelia, Monterrey and Guadalajara's arch-rivals America already qualified.
Guadalajara went on a five-match unbeaten run immediately after Dutch great Cruyff's appointment, which was aimed essentially at an overhaul of the western club's youth scheme.
British media reports have linked Cruyff with the director of football post vacated by Damien Comolli at Liverpool.
The Mexicans came unstuck in the Libertadores Cup, South America's Champions League, in which they play as guests and were runners-up two years ago.
A 1-0 defeat by Uruguay's Defensor Sporting at the end of March heralded a run of five defeats in domestic and international competition including a 1-0 home loss to the Azteca stadium-based America in the "clasico", Mexico's biggest match two weeks ago.
"[The players] feel frustrated because they made great efforts, they didn't deserve this," Guadalajara's sporting director Rafael Ortega said after Saturday's defeat.
"It pains me what's happening with Chivas but we'll keep fighting and working to improve," he told Guadalajara's official website.
"We made a bad start to the championship, that's what affected us," he added in reference to Chivas taking only two points from their first seven matches.
Guadalajara struck their first goal in five matches through winger Omar Arellano in the 21st minute on Saturday as they had the better of the first half at the Universitario but Chivas had striker Erick Torres sent off in the 37th for a stamp on defender Israel Jimenez.
The second half turned into a nightmare for Guadalajara as their qualifying hopes all but ended. Carlos Salcido equalised for Tigres in the 72nd and within a minute Chivas forward Marco Fabian was dismissed for a second booking.
Brazilian central defender Juninho headed the winner from Argentine playmaker Lucas Lobos's cross in added time and Guadalajara's Jesus Sanchez was shown the red card for dissent.
