The defending champions returned to La Liga action after a commendable 1-0 win over Serie A giants Juventus in the UEFA Champions League on Wednesday.
But, against Nuno Espirito Santo's Valencia, Atletico were met by a side who produced a storming start to the match at the Mestalla, scoring three times in the opening 13 minutes.
A Miranda own goal was swiftly followed by a fine Andre Gomes solo effort and a Nicolas Otamendi header before Mario Mandzukic gave Atletico a glimmer of hope in the 29th minute.
Atletico wasted a major lifeline just before the break as Diego Alves saved Guilherme Siqueira's penalty, but Simeone could not fault his players' effort.
"Atletico lost with courage," he is quoted as saying by AS.
"We worked and we kept running. Valencia aren't in Europe and you could see that.
"They would have to have a really bad season not to be third or fourth [in La Liga].
"The match lasted 94 minutes. Valencia started strong, we made mistakes we don't usually make and they took advantage.
"After that, Atletico had a very good game. I'm happy with the team's work. Those 10 minutes did a lot of damage but I'm proud of what my team did.
"There are times when there's dignity in giving everything on the pitch."
Many were surprised when full-back Siqueira stepped up to take Atletico's penalty just before the break ahead of Mandzukic, but Simeone took responsibility for the decision.
"Mandzukic is the taker but I asked Siqueira to take it instead," the Argentinian added.
"He's missed two penalties in his career and both have been for Atletico.
"I think the referee did very well. He gave a penalty that was hard to see and none of his decisions were decisive."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.