Athletic had a 1-0 lead through Mikel Jauregizar before goalkeeper Julen Agirrezabala was sent off on 83 minutes. An error from replacement Alex Padilla saw Sevilla grab an injury-time equaliser.
Valverde said, "When you draw it all depends on who scores the equaliser. If you get the equaliser it feels better. On the other hand, if the other team scores, it feels like the points have escaped you.
"It was a circumstance of the match. The game seemed over and done but the sending off was key. That and the goal. It was a hard-fought match. They started very well and, afterwards, we were better.
"It was a shame. Points have escaped us at home in some strange situations. Sevilla are a great team, they never gave up and we have to keep going."
He added: "For us it's not a sending-off, because Julen touches the ball and it bounces away. Then he touches the player. They checked the situation and decided to send the player off. They called a foul and sent him off."