The 3-1 victory over UAE at Wembley was Team GB's first of London 2012 and therefore their first at an Olympics for 52 years, while captain Giggs became the oldest scorer in the tournament's 88-year history when he gave them a half-time lead.
Giggs and fellow Welshmen Craig Bellamy and Joe Allen caused a row during the opening 1-1 draw against Senegal on Thursday by not singing God Save the Queen. They were silent during the anthems again on Sunday night and Giggs said afterwards: "It's a personal thing. The British anthem is the same for a Welshman, Scotsman or an Englishman."
He added: "It's difficult but it's not an issue for us. It might be for other people but, once the game starts, we're all pulling in the same direction and I think that's the main thing."
Team GB's final group game against Uruguay takes place at Cardiff's Millennium Stadium where Giggs, Bellamy and Allen can expect a hero's welcome.
The national anthem may not be so warmly received in the Welsh capital. I hope it won't get booed and I hope the fans will get behind us as they have in our first two games," Giggs said.
"It will mean a lot to all of the Welsh lads to play in our own stadium, our own back yard so it will be a great occasion."
Giggs broke an 88-year-old record by netting at the age of 38 years and 243 days.
UAE equalised before Scott Sinclair scored with his first touch and fellow substitute Daniel Sturridge also netted.
Giggs added: "It was a very important win, especially after the Senegal result and the pressure was on. I'm still disappointed not to play in a World Cup, a Euros or a major tournament and now this is something I'm relishing."
- Craig Bellamy