Antonio Conte's men needed a 94th minute winner to secure all three points against the Spanish side.
Chelsea now sit three points clear at the top of Champions League Group C.
Atletico away was arguably the Blues' hardest test in the opening round of the competition.
But opposition boss Simeone believes they were deserving of their three points at the Wanda Metropolitano.
“Chelsea? They were better than us," admitted the Argentinian after the game.
"Tactically and physically, they were always more comfortable.
“Hazard and Morata? Chelsea had a good game overall, they were very competitive and strong. They won well and deservedly so.
“The defeat? We took it as it happened, Saul had a chance to put us 2-0 up, but they were better, tactically and physically with intensity. Chelsea have to be congratulated.
While Chelsea are already close to securing their place in the knockout rounds, Atletico are yet to win in the competition this season.
Los Colchoneros still have to entertain Italian outfit Roma at home and face the Premier League champions at Stamford Bridge.
However, Simone is confident his team will still progress.
“All we can do is keep growing and improve in every aspect, and surely the win will come," he added.
“Roma? If we’d lost to them, it would’ve been the same.”
Chelsea welcome Roma to West London in the next round of fixtures.
