The AC Milan striker's header with 12 minutes to go sent France through to Wednesday's semi-final as Harry Kane missed a late penalty, his second of the match.
Kane had levelled from the spot shortly after half-time, cancelling out Aurelien Tchouameni's brilliant long-range effort that gave France the lead on 17 minutes.
"It's extraordinary. We worked really hard defensively when we were ahead. It reminds me of Belgium in 2018," said Giroud, referring to France's 1-0 win in the semi-finals four years ago in Russia.
"Unfortunately we conceded the penalty. But we were able to be dangerous on a few occasions at the end of the match."
"You always have to believe and (Antoine) Griezmann gave me a great ball (for the goal)."
"I'm so proud. We pulled out a big performance tonight," he added.
"We knew the potential of this young English generation. They've got it all. We had to use our mental strength to get over the line."
