Álex Berenguer and Robert Navarro struck either side of the 20-minute mark to give Edin Terzic's side control, and Celta never recovered despite a wholesale reshuffle at the break.
Giráldez made four of his five permitted substitutions at half-time, reasoning: "I would have changed everyone at the break. I made four changes because we have five and it seemed like too many to make all five."
The Celta Vigo boss did not spare his own team in his assessment of the display.
"A 0-2 at home, with the feeling we had from the 0-1 onwards, is a disaster in my view. We have to change a lot of things to be able to compete the way I think we did in the first half hour of the second half," he said. "When you don't defend in an organised, intense way against a team of Athletic's level, it's normal to concede five, and they came close at times. We were very poor defensively, in a low block - once we go behind, we want to rush to get out of it instead of organising ourselves."
Asked whether transfer-market distractions were a factor, Giráldez was dismissive.
"We are professionals. If that's the excuse, we have a problem and we'd be better off doing something else. I didn't like anything about the first half except the first 10-15 minutes," he said, before insisting reinforcements were still needed before Tuesday's deadline.
"There's still a market, we'll see how it develops. We're a little short of numbers in those positions. It's important because we're going to play a lot of matches at this crazy rhythm we've started with. We need a bit of stability back there."
Terzic, celebrating his first win at Balaídos, could not hide his satisfaction.
"I'm happy, above all with the performance of the whole team. The first half was really good, with high pressing. I'm very happy as a coach. The performance was almost perfect, though there were also some errors," he said, praising his side's control after Celta's early spell of pressure.
"What we did was press really well. We were very compact and won a lot of balls in midfield. That's the way we need to continue and what we want to achieve in the coming matches."
The German singled out Íñigo Ruiz de Galarreta, involved in both goals and making his first league start for Athletic Club of the season.
"He's played a very important role and it's worked really well. He brings calm and composure, but his game was also almost perfect positionally," Terzic said, before addressing the squad's earlier media protest that did not continue this week.
"It's not a matter for me, it's an internal matter and it should stay that way. The team's performance was also a statement."