The Atletico coach was devastated that his side was defeated in extra time by Real Madrid, while he avoided criticizing the referee or Raphael Varane despite a late clash.
The coach was fuming on the sidelines over the five added minutes in the second half in which Sergio Ramos scored his dramatic equalizer to send the match into extra-time.
Having remonstrated with the referee after 105 minutes had been played, Simeone then stormed on to the pitch after becoming riled by Madrid defender Raphael Varane, who seemed to provoke the Atletico bench by kicking a ball into the dugout following Cristiano Ronaldo's late penalty.
"I don't feel sad," the Argentine told reporters after the match. "It's bitterness that I feel for not reaching my goal. Now the calmness is stronger and it has overcome this situation. The match ends when the referee wants, I've nothing else to say on the matter. Hopefully this will provide Varane with experience and he will learn. He's a great player with a great future."
Gareth Bale, Marcelo and Ronaldo all scored in extra time to give the Blancos a flattering scoreline considering how long Atletico had led, but Simeone accepted that his team grew weary as the game went on at Estadio da Luz.
"Real Madrid were better in the second half of the game" he added. "We were all tired but they got a little better. I tried to tell my team that they remained competitive throughout the match and I am always proud of my players — they fought until the end with a lot of humility.
"We were locked in the middle of the pitch with nowhere to go and that makes things very difficult. Football is marvelous for that. At times, it teaches us that winning is everything and it is the most important. Losing is not worthy of a tear, we need to keep our heads up and prepare for next season. It is part of the game but obviously you have the two situations. But we gave everything and other people know that Atletico can compete.
"We're working for the best. We won a marvelous Liga, which is day to day, and we came close to an international competition, which is good for business."
Simeone also defended his decision to start Diego Costa, who has been struggling with fitness issues in recent weeks, after the forward had to be brought off after nine minutes.
"The responsibility to play Costa was mine," he added. "I was wrong but he was not in the good condition that we saw yesterday."