Simeone's side won the second-leg in Madrid 1-0 thanks to Koke's fifth-minute goal to win the tie 2-1 against their La Liga rivals.
And the Atletico boss paid tribute to the home fans for their support throughout Wednesday's match.
"The atmosphere was amazing," he said. "It didn't affect Barca because they are used to those atmospheres, but it did influence our players. It gave us great positive energy."
Simeone also paid tribute to the effort put in by his players.
"When someone is working like they are working there are times when you don't need many words," said the Argentine.
"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."
Goalscorer Koke also praised both the Atletico fans and his team-mates for the way they performed over both legs of the tie.
"With these fans behind us it is very hard for us to lose a match here," he said.
"The work of the team across both legs has been spectacular.
"We ran a huge amount, we played the two games in the way we wanted and I think we were the deserved winners."
The victory means Atletico are into the semi-finals of Europe's premier club competition for the first time in 40 years.
It is also the first time in the last seven seasons that Barca have not reached the last four of the tournament.
They are joined in the last four by Madrid rivals Real, Premier League side Chelsea and German holders Bayern Munich, who beat Manchester United 3-1 on Wednesday to seal a 4-2 aggregate victory over David Moyes' side.
"We maintain the same humility," added Simeone. "We understand that the other teams (in the semi-finals) have been there far more than Atletico Madrid.
"We are there 40 years later and we believe in what we are doing. We want to continue being competitive as was our intention at the start."