Koke scored the winner in the second period for the capital outfit, who became just the second team in La Liga to secure all three points at San Mames this season.
"We are aware of our great performance. It's been one of the best in the league," Simeone told reporters at a press conference.
"We recovered the ball very clearly and were also clear in taking advantage of the gaps for Diego [Costa].
"We always knew how to play, we were always strong. The team overcame the adversity, from the game, from the commitment and from the intensity, to win a great match."
Atletico face Barcelona in the quarter-finals of the Champions League on Tuesday.