Manchester United great Giggs, a former Wales captain, was in no doubt of the significance of his country’s win, which set up a semi-final against Portugal.

“I’m so proud,” said the 42-year-old Giggs.

“It’s quite simply the greatest night in Welsh football history, the best result in Welsh football history but more impressively, it was the best performance.

“To make a team ranked second in the world look so ordinary and in the end win comfortably is very impressive.

Dragon roars: Wales stun Belgium 3-1 to reach Euro 2016 semi-finals

“They were the better team in every area – defensively, offensively, they won every challenge, and they looked comfortable.

“Of course Belgium had their moments, but so did Wales. And three fantastic goals,” he added of well-taken efforts by skipper Ashley Williams, Hal Robson-Kanu and Sam Vokes, all of which came after Radja Nainggolan gave Belgium a 13th minute lead.

Wales coach Chris Coleman said the feeling of beating Belgium was “indescribable” as he insisted his team had shown themselves to be capable of beating any opponent.

“We dream about nights like this and we’re never sure whether you’re going to be good enough or lucky enough to be involved in an experience like that,” said an emotional Coleman after the game.

“If you are lucky enough to be involved in it, it’s indescribable really.

“You need a bit of talent of course but you have to work hard and that’s what we’ve done and we find ourselves in an incredible position.”

Portugal reach Euro 2016 semi-finals after beating Poland on penalties - and they still haven’t won a game in normal time

Wales were deserved winners against a supremely talented Belgium side and triumphed despite star man Gareth Bale not having his best game at the tournament.

Coleman added: “It wasn’t as if it was smash, bang, wallop and we just nicked the result, because we didn’t. We took the game to Belgium for long periods.

“We played very well and when we needed to defend we defended like soldiers. I thought our performance was fantastic and I thought we thoroughly deserved it.”

Their reward is a semi-final showdown with Cristiano Ronaldo’s Portugal in Lyon next week and Coleman urged his side to remember how far they have come in a short space of time.

“The whole experience for us is uncharted territory – 1958 was our last time, a long long time (ago),” said Coleman after seeing Wales become the first British nation to reach the last four at a major tournament since England on home soil at Euro 96.

“All we can do is keep reiterating to the players to never forget what it’s taken for us to be here in this position, never forget what we’ve had to do and what our beliefs and our identity are.

“I’d imagine there are three million people back home going absolutely crazy and they deserve that.

“I said in the campaign when we were on top after five games in qualifying to not expect anything from us, to get carried away.

“I know my team are good enough to perform against anybody – I knew that before tonight.

“The fact we are in the semi-final is absolutely fantastic but we have to approach our next game just by taking care of our own performance.”

However, having finished top of group B ahead of England and then edged out Northern Ireland before beating Belgium, Coleman insisted that any thoughts about winning the tournament itself are banned for now.

“I have never thought about that and I promise you my players and staff won’t be thinking about winning the tournament – we are only thinking about our next challenge which is Portugal.”