Celta couldn't take advantage of Pablo Barrios' dismissal as Iago Aspas' penalty was pegged back by Atletico's Alexander Sorloth.
Giraldez said afterwards: "Drawing at the Metropolitano is a good result.
"Getting four points out of six against Betis and Atlético is obviously a good result, but I leave with the feeling that we could have gotten six out of six and that we wasted minutes of the game, misinterpreting how to attack.
"We improved throughout the game, creating more chances and opportunities, but we had chances to kill them off and we weren't able to get them right, and in a vertical attack we lose two points."
He also stated: "After the expulsion and before they adjusted their game, we were not able to attack in an orderly, sensible and calm manner. Surely until the 25-30 minute mark of the first half. It was hard for us to understand that the ball had to go inside.
"In the second half there were moments when we were unable to get out of their first pressure. It's a shame that we didn't convert the 0-2, which would have been decisive in winning."