Following a 1-1 draw at Camp Nou, Atletico won 1-0 at the Vicente Calderon to reach the semi-finals and deny Barcelona a seventh successive appearance in the last four of the UEFA Champions League.
"There's a lot of joy at having got through a tie against great rivals who have a proud history," Simeone said.
"Now we are calm because we know this isn't the end, and we will try to recover as soon as possible because on Sunday we have another match.
"The first 20 minutes were very good in terms of our attitude, intensity and play. Then Barca began to get into the game and had some opportunities, so things became trickier for us.
"My players don't need words to motivate them – they need security, decisiveness and the ability to try and get the best out of them all. I admire these players. I admire their dedication and the way they work together as a team.”
Adrian, who only played after Atletico goal machine Diego Costa failed to recover from a hamstring injury, hit the crossbar, set up the only goal for Koke, and proved a constant torment to Barcelona until his withdrawal on the hour-mark.
Simeone hailed the 26-year-old and said the forward could play a big part late in their campaign.
"Adrian was great in the first half," he said.
"He almost scored and he linked up perfectly with Koke and David Villa.
"Aside from getting through the tie, I'm happy that Adrian is back to his best. I repeat: Adrian is a different player now and one that can give us alternatives."
