Álvaro Morata put Atletico ahead after just four minutes at the Metropolitano stadium, before Antoine Griezmann made it 2-0. Toni Kroos pulled a goal back for Real, but Morata's header within a minute of play resuming after half-time secured the three points for Atletico.
"[The problem] was defensive fragility, which we haven't had in our first few games," Ancelotti said in his post-match news conference. "In six games [this season] we had conceded three goals, and today we conceded three in 45 minutes.
"We were fragile, it wasn't a good night in defence. I won't go into individuals, but we didn't defend well. The goals were photocopies [of each other], they split the centre=backs and we weren't well positioned. We weren't compact."
With Vinícius Júnior dropping out of the Real Madrid squad on the day of the game, delaying his return from injury, Ancelotti opted to play Jude Bellingham as a forward alongside Rodrygo with Luka Modric and Toni Kroos both starting in midfield for the first time this season.
"The formation didn't change," Ancelotti said. "We started with Modric at number 10 and two forwards, Bellingham and Rodrygo. Maybe I could have done better, when the team doesn't do what it could have done, obviously that's my responsibility. But I've got wide shoulders, that's no problem."
Ancelotti said he'd stick with his midfield diamond for Madrid's next game, hosting Las Palmas on Wednesday.
"The problem isn't the formation," he said. "The formation won't change. We're sad and angry as always when we lose, but up to now we've done well."
Atletico coach Diego Simeone praised his team's performance and that of Morata, who has now scored five goals in LaLiga.
"Alvaro played an extraordinary game," Simeone said. "We need this Morata. We know he can do it. We know he has the tools to get the numbers we need. Let's hope he can maintain this level, because for Spain and for Atletico Madrid he's an important forward.
"I'm very happy for the fans," Morata said. "The atmosphere was incredible. We were all together, us on the pitch and them in the stands.
"Tomorrow kids can go to school wearing their Atletico shirts and be proud of us."