An early penalty converted by Kike Garcia had Alaves ahead before Celta equalised in the second-half through Pablo Duran.
Afterwards, Giraldez said: “It was a very competitive match and at times the point was not enough for us. I am happy with the team's reaction against Rayo and today. The point is good for us to add points and to be able to continue improving. We have gone from less to more.
“We have played two away games and in the third minute we had an unfortunate action against us. The referee went to see the VAR, which I think is a good thing. He decided it was a penalty, so it is a penalty.
"Obviously, the goal we conceded, on a psychological level, changes our game plan a lot. In the third minute and on such a difficult pitch and with such a pressing opponent. It's difficult to start off the same way again. In the second half we were much more convinced. We looked to do damage. We competed very well. Last year they ran over us, they scored three against us. We needed to compete better in the first half."
He added: "I'm happy that we didn't get sunk in difficult situations at the start of the game and that we have the contribution from the bench that we had today and the feeling that we could have won the game."