Wales reached the semi-finals in France after ending a 58-year wait to play at a major tournament, with football fever gripping the nation like never before.
Giggs' side will book their place at Euro 2020 by beating Hungary in Cardiff on Tuesday, ensuring there is no need for the play-off spot which they have already secured.
Asked whether qualification would atone for his failure to grace a major tournament as a player, Giggs said: "It's not about me. It's about the country as a whole.
"The team in 2016, everyone, whether you were involved or a fan or watching on TV, it was amazing.
"If we can recreate that atmosphere, it's fantastic. It's not about individuals. As a player, that's over now. Now I'm a manager.
"I think we've put ourselves in a great position. We've still got one game to go and a tough game, so we'll need to win that to qualify."
Giggs was an unpopular choice among many Wales fans to succeed Chris Coleman in January 2018.
The former Manchester United player has often had his poor attendance record as a Wales player held against him.
But Giggs has won over some of his critics during a five-game unbeaten run, which has shown steady signs of progress and taken Wales to the brink of Euro 2020 qualification.
"We just need to show the quality we've shown lately," he said. "We have got that momentum. I think we'll have to be better than we were the other night (when Wales beat Azerbaijan 2-0 away) if we are going to win.
"But I believe in the players. I believe in the group that we've got and the qualities they possess.
"Experience counts for a lot, but what I've seen in the young players is coming in and being fearless. So they help each other.
"The younger players can inspire the older players and vice versa.
"We've got a good balance of players who've been there and done it, and also players who are hungry to recreate what the other lads did in 2016."
Gareth Bale and Aaron Ramsey are both available after coming through the Azerbaijan game unscathed after their recent injury problems.
Skipper Bale played an hour in Baku before being replaced by Ramsey, who was making his first appearance in Euro 2020 qualifying.
Ramsey has yet to play 90 minutes this season and might be used as an option from the bench again, but Joe Allen is set to return from suspension to replace Joe Morrell.
"As always, it's a bit of a balancing act," Giggs said. "The players you more or less know who won't be able to do 90 minutes, and that will impact on the selection."