Julian Alvarez struck on 90 minutes for Atletico's winner.
Giraldez later said: "I can acknowledge all the merits we have made, all the things we have done well, but I am leaving angry and with the feeling that we have to demand more from ourselves and that we can demand more from ourselves. The normal thing is that you win this match and we have not done that.
"There were situations, at certain times in the second half, in which we threw the ball away when we should have dominated them even more, done more damage to them.
"I'm proud of the team, proud of what we've done, giving credit to the difficulty of being superior, in my opinion, against one of the best teams in the world. I think what we wanted to happen happened and it's a shame that the result wasn't what we wanted."