The France international scored an excellent consolation goal past the Spaniard deep into stoppage time, but it was not enough to prevent the Gunners slumping to a 2-1 defeat.
That was Giroud's first cameo appearance since suffering a foot injury on the second weekend of the season - and the 28-year-old believes it was an important moment for his confidence.
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Giroud: It was a turning point
Asked by Arsenal's official website if it felt like a turning point, Giroud said: "I think so. It was an incredible feeling. I am back, I come on, I am running everywhere and I hit that volley that goes straight into the top corner!"
He went on to reveal what De Gea said to him after the full-time whistle; with the Real Madrid target admitting he couldn't get near the strike.
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Giroud: De Gea said this to me
"David de Gea came to me after the game and told me: “Well done, there was nothing I could do!” Giroud added. "It was nice although I would have rather us winning or drawing the game. I had so much energy in me. I needed something like that. Since moving here, it is true that I hadn’t scored much against teams from the top five so on that level, it was important as well."
Giroud has scored an impressive 14 goals in 24 appearances for the Gunners this season and remains the club's first-choice centre-forward, despite the summer arrival of Danny Welbeck from Manchester United.
His presence, strength and aerial ability makes him an ideal target-man, while his technical qualities with the ball at his feet are sometimes underrated.
Very few strikers would be an upgrade on Giroud
Arsenal are continually linked with new strikers, but very few forwards would be an upgrade on Giroud for the north London outfit.
In terms of realistic transfer targets, perhaps the only striker who would potentially be an upgrade is Lyon's Alexandre Lacazette, the 23-year-old who has scored 27 goals in 32 appearances this term.
An international teammate of Giroud's, Lacazette is fast, powerful and possesses an unerring eye for goal.
Question marks remain over Giroud's ability to convert chances at the first time of asking. His recent performance against AS Monaco in the Champions League last-16 first leg - arguably the Gunners' most important match of the season so far - was heavily criticised after he missed several gilt-edged opportunities.
He will, however, have a chance to make amends when Arsenal take on Monaco for the second time on Tuesday night.
Arsenal fans: would you replace Olivier Giroud this summer? If so, which striker should Arsene Wenger sign? Have your say in the comments below!