Iago Aspas and Hugo Alvarez struck the goals on Friday.
Giraldez said afterwards: "At times it seemed like we were playing with twelve players. The atmosphere was spectacular, they helped us a lot.
“It was a very complex game against a very complete and uncomfortable opponent. I think we were serious, competitive and knew how to take advantage of the chances we had in the final third.
"I am left with the feeling that whoever comes out, the fans help them and they perform and compete. In the second half I think we were better.”
On Antonio Raillo's dismissal for Mallorca, he added: "For me it's a red card, it's a situation of the last player. Our player who is more advanced against their player who is more backward.
"A very fast player like Douvikas who is difficult for anyone to catch. I understand the protest, it's a situation on the edge."