Simeone: Atletico's display 'one of the best'
The league leaders had to come from behind at San Mames, but the victory kept them a point clear of Barcelona and three ahead of Real Madrid.
Simeone was delighted with the performance as Atletico prepare for their UEFA Champions League quarter-final first leg against Barcelona on Tuesday.
"We are aware of our great match. It's been one of the best in the league," the Argentine said.
"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."
Iker Muniain gave Bilbao a sixth-minute lead before Costa struck and Koke, who set up the equaliser, netted what proved to be the winner early in the second half.
Simeone said Costa was a key for his side, with his energy drawing particular praise.
"He's a guy who keeps growing day by day, he has an enormous physical strength," he said.
"He infects his team mated with this thing he has and they exploit it in the best possible way."
As he has all season, Simeone said it was important for his team to enjoy the moment and not look too far ahead.
"We enjoy this situation day by day, minute by minute, training by training, match by match," Simeone said.
"That's where we feel strong and we'll stay that way because we can't leave this line of action."