Barca were unable to cope with a fired-up Atletico in the opening 20 minutes of the Champions League quarter-final, second leg at the Calderon, when Koke scored the only goal of the game in the fifth minute to secure a 2-1 aggregate success.
Although Barca improved in the second half, Atletico turned in a brilliant defensive display, almost scoring several times on the counter-attack, to claim their place in the last four of Europe's elite competition for the first time in four decades.
It was a classic smash and grab raid and Atletico's gutsy performance was typical of a side who take inspiration from a coach who as a combative and never-say-die midfielder was said to play "with a knife between his teeth".
"I think the first half, those opening 20 minutes, were very good due to our aggression, our speed, our focus, our commitment," Simeone said.
"Later on, obviously Barcelona started to grow into the game, above all they had more of the ball," added the 43-year-old, who has transformed Atletico into genuine contenders in Spain and Europe since taking over at the end of 2011.
"I don't know if they had many chances but the crosses coming over quickly from (Daniel) Alves on the right were causing us a few problems.
"Later in the second half it was a matter of winding down the clock and waiting for a chance to counter attack and look for the second goal to calm things down."
It was one of the greatest nights in Atletico's history and their fans packed into the arena next to the Manzanares river were thoroughly enjoying another excellent performance in the club's best season since they won a La Liga and Copa del Rey double with Simeone in the team in 1996.
Simeone paid tribute to his players, who were visibly tiring in the latter stages but dug deep to keep waves of Barca attacks at bay.
"When someone is working like they are working there are times when you don't need many words," Simeone said.
"The truth is I have admiration for these players beyond the affection I have for them as people.
"I admire the way they sacrifice themselves, the way they work for the team and never betray it.
"That is priceless because in the history of all battles and all wars the best don't win but those who fight better strategically. And we try to be a bit like that."
Atletico go into Friday's draw for the two-legged semi-finals, which take place later this month, along with neighbours Real Madrid, Chelsea and holders Bayern Munich.
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