Former Mexico striker Francisco Fonseca broke his 11-month goal drought by scoring twice as Atlante's "Iron Colts" hit four in 21 first-half minutes in Saturday night's match at Pachuca's Hidalgo stadium.
The chances of Flores - Mexico's caretaker coach for three friendlies after last year's World Cup - steering 2010 Concacaf Champions League winners Pachuca to the last eight look slim with the team bottom of Group Two.
The top two teams in each of the three groups and the next two best-placed teams in the overall standings at the end of the 17-match round robin phase qualify for the quarter-finals. Pachuca have won two and lost five of their 10 matches.
Pachuca's Colombian international goalkeeper, Miguel Calero, who came off injured after Fonseca's second goal in the 41st minute, said he would have surgery on his left arm and be out for the rest of the season.
"I've decided, I'm going to have an operation," said Calero, who will be 40 next month. "I'll recover, do a good pre-season and play again.
"It's an internal fibrosis that prevents me from working properly and I can't play like this," Calero, who has been at Pachuca since 2000, told reporters.
Pumas UNAM, the only unbeaten team with 21 points from nine matches, were playing Morelia, on 18 points, in a clash between the top two teams in Group Three on Sunday.
Cruz Azul, third in the group, were away to Group Two leaders America in the so-called "Clasico joven" (junior classic) at the Azteca.
Tigres UANL, held 1-1 at home by San Luis on Saturday, have a three-point lead over title holders Monterrey in Group One. Monterrey, winners of the Apertura championship in the first half of the season, beat Necaxa 1-0 away on Friday.
