Chelsea came from behind and produced a last-gasp 2-1 victory when substitute Michy Batshuayi scored with a stoppage time strike.
Atletico had gone ahead in the first half when Antoine Griezmann converted from the penalty spot.
While Simeone thought the La Liga giants had a chance to kill the game off through Saul Niguez, he had no complaints about the result.
“The opponent was the better team, they were the more comfortable team in all moments, and deserved to win,” Simeone said.
“They played a good game in general, they are a very strong and competitive team, showed their status.
“In the first half we had the chance from Saul to make it 2-0 but we were never comfortable.
“They were better tactically, technically, physically, with intensity.
“You must congratulate a team who played as Chelsea did today.
“A draw was good for us, they had patience in the last play to move the ball very well and end the game very well for them.”
Griezmann agreed with his manager’s assessment, as he said: “They were the better team in every aspect.
“There is nothing else to say. We must try and win all our games now.
“In the first half they were on top of us, and in the second half they were better [too]. Maybe we lacked a better game from me.”
Chelsea, who top Group C, next face Roma in back-to-back Champions League games.
Costa and Conte hug… but it’s the wrong Conte
DIEGO Costa hugs a Conte, but it’s not Antonio, Neymar and Edinson Cavani put their penalty drama aside, and David Luiz is slammed for “cheating”.
Days after completing move to Atletico Madrid, football fans were wondering what would happen if Diego Costa came face-to-face with Antonio Conte.
Atletico Madrid’s new striker did embrace Conte – it just wasn’t Antonio.
Costa was pictured hugging Antonio’s brother Gianluca before he watched from the stands as Atletico went down 2-1 to the Blues after Michy Batshuayi’s dramatic injury-time winner.
Neymar and Edinson Cavani were on fire against Bayern Munich, and no battle over who takes the penalties was reignited in the 3-0 victory.
Instead, the duo were pictured embracing during the match.
Over in Lisbon, Lionel Messi, who sparked Barcelona’s only goal with a free kick against Sporting, was also pictured in an embrace with a fan.
The supporter stormed the pitch to meet his idol and the Argentine didn’t turn him away – maybe because he was nice enough to do up his shoelace.
KEANE SLAMS LUIZ: IT’S MADNESS REALLY. IT’S A FORM OF CHEATING
Former Manchester United midfielder Roy Keane blasted David Luiz’s “lazy” act after the penalty he gave away almost cost Chelsea the result.
The Brazilian defender was penalised for an obvious grab of Lucas Hernandez’s shirt, before Antoine Griezmann stepped up to give Atletico a 1-0 lead in the 40th minute.
“It’s madness really. It’s a form of cheating,” Keane told ITV.
“Why he’s doing it is beyond me. He’s lazy and he’s letting his teammates down. He knows himself. There’s no need. We see a lot of that going on, so I’m glad he got punished for it. It’s a form of cheating.”