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.