Host Espanyol's 2-1 win on Sunday was Atletico's first opening defeat since Simeone took over in late 2011. They hadn't previously lost a day-one La Liga game since 2009.
Simeone started the match with five of the club's new signings for the season but it was Julian Alvarez, who scored 17 times in the league last season. who gave Atletico the lead in the 37th minute from a free kick.
But they were stunned on the road by goals from Miguel Rubio in the 73rd and Pere Milla in the 84th.
"It happens," Simeone said.
"The result hurts, but it's going to make us improve and grow. I'm left with all the good things the team did."
Last season, Atletico only twice lost a league match they were leading.
Elsewhere, Nico Williams led Athletic Bilbao to a 3-2 win over Sevilla.
Williams, who had been linked with a move away from his boyhood club and to Barcelona in the off-season, put the hosts ahead by converting a 36th-minute penalty kick.
Athletic, coming off a fourth-placed finish last season, added to the lead thanks to Maroan Sannadi in the 43rd before Sevilla rallied with goals by Dodi Lukebakio in the 60th and Lucien Agoume in the 72nd.
Robert Navarro put Athletic back in front for good in the 81st.
Getafe scored a 2-0 win at Celta Vigo with second-half goals from Adrian Liso and Christantus Uche.
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