Leipzig will play Paris Saint-Germain in the semi-finals on Tuesday after Tyler Adams’ deflected shot in the 88th minute earned them a shock 2-1 victory in Lisbon.
Atletico’s Joao Felix had earlier scored a penalty to cancel out Dani Olmo’s opener.
Defeat ends a disappointing season for Atletico, who finished third in La Liga, 17 points behind Real Madrid.
“We didn’t have that physical sharpness or rhythm,” said Simeone afterwards.
“At the end of a season with so much pressure, so much need to get into the Champions League, and the need to integrate new players.
“We came with a lot of hope. The feeling is a lot of bitterness but I know the players gave everything. They gave it their all.”
Questions will be asked about Simeone’s future and his ability to turn this Atletico side into winners again, while sticking to his defensive style of play.
“I have nothing to say to anyone about what we did this season. It’s a good season, third in La Liga, quarter-finalists in Champions League,” Simeone said.
“Next season will be tough, very tough.”
Simeone admitted Leipzig were the better team and deserved to go through to the semis.
“They were better, faster,” he added. “We gave everything and we leave with dignity, with an opponent who deserves their victory.”