Atletico Madrid overcame the Basques to book their place in the semi-final of the Copa del Rey and the Argentine believes that either side could have won
The current holders of the competition became the first team to win at the new San Mames this term after Diego Costa's late goal sealed a late comeback.
The Argentine was full of praise for Athletic, though, and believes the tie could have gone either way following his side's first-leg 1-0 victory at the Vicente Calderon.
"We have played against a great rival. Athletic Bilbao have an amazing team," Simeone told reporters.
"I can tell you that in the first 30 minutes we had control of the pitch, but not the ball, and we had a great opportunity when Diego Costa was one-on-one with the goalkeeper after just five minutes.
"Also, there was a chance for Raul Garcia, but in the last 10 minutes of the first half, Athletic had great opportunities.
"In the second half we started very strong and well, then we scored a goal which gave us much more confidence, strength, and we won a game in a very difficult stadium."
Atletico now face city rivals Real Madrid, whom they beat in the final of the competition last season, in the last four.