Promoted Xerez came from behind to beat Villarreal 2-1 and notch up their first ever la Liga victory, sending the visitors to the foot of the standings.
Atletico were torn apart 3-0 by Osasuna, conceding all three goals inside the first half hour in Pamplona.
Against the run of play, Xerez scored a controversial winner 10 minutes from time when Villarreal goalkeeper Diego Lopez's clearance struck an attacker's arm and Antonito lobbed the ball back into the empty net.
"We were lucky but you have to go looking for luck," Xerez coach Jose Angel Ziganda told reporters.
"This is a small step, but very important from a psychological point of view...now we aren't bottom anymore."
Valverde bemoaned the referee's decision for the winning goal and brushed off questions over his future.
"Coaches are always playing for their positions," he said. "Now we are bottom and we can't go down any further so the only way is up."
Atletico's defence was unable to cope with the aerial power of Walter Pandiani against Osasuna, the Uruguayan striker diving to head the first after only four minutes.
He headed his second from a free kick in the 25th minute and Carlos Aranda put away the third four minutes later to leave Atletico with just one league win this season. Abel Resino's side lie 15th with six points from seven matches.
