Atletico's La Liga win over Sevilla last weekend had raised hopes of a revival after a poor start to the season, but they were two goals behind and down to 10 men inside half an hour against Recre, who are 15th in the second-division standings.
"The blame is all mine," defender Tomas Ujfalusi, who was shown a straight red card for a late tackle in the 20th minute, said on Atletico's website.
"I believe that the fault was mine because after the sending off everything was more difficult for the team," he added.
Sanchez Flores, brought in to replace the sacked Abel Resino at the end of October, had some harsh words for the team at the end of the match and said he would be looking to find players who did not let him down.
"I want to ask the forgiveness of the supporters for such a huge disappointment," he said.
"At no point were we able to read the game," he added. "This is not what the history of Atletico Madrid is about, nor that of their fans."
Defender Alvaro Dominguez said the players needed to take a long, hard look at themselves and come up with ways of turning things around for next week's second leg at the Calderon.
"It's impossible to explain how we let in so many goals," he said. "It's logical that our fans are upset and I am embarrassed at the way we played," he added. "But we are Atletico Madrid and we'll unite to try to turn this tie around."
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