But Chris Coleman's side eclipsed that achievement by overturning Radja Nainggolan's thunderous early strike in Lille with goals from skipper Ashley Williams, Hal Robson-Kanu and Sam Vokes.
His players rose to the occasion wonderfully, recovering from a hard start to claim what must rank as the greatest win in Welsh football history.
They have become the first team to reach the semifinal on their European Championship debut since Sweden in 1992 and have scored 10 goals along the way.
"The fans here and the fans back at home have been incredible".
When asked about Messi and Ronaldo he told reporters: "They are both world-class players".
"I think if you're lucky enough to be involved in that, it's indescribable, really".
Ramsey took his tally of assists at the tournament to four, joint-level with Chelsea's Eden Hazard, as he laid on two in the comeback win over Belgium.
Wales came back from a goal down to beat Belgium 3-1 here on Friday night to make the cut although it was Belgium who had gone into the tie as favourites.
"It wasn't as if it was smash, bang, wallop and we just nicked the result, because we didn't", Coleman added.
Wales defender James Chester added it is a "blow" for his side to be without Davies and Ramsey for the country's first semi-final at a major global tournament.
Wales will now face Ronaldo's Portugal in EURO 2016 semi-final, but they will be missing one of their most important players, Aaron Ramsey. We made mistakes we shouldn't have made.
"We said before the game tonight that one or two of the boys were on yellows but we've got to do what we need to do to get through".
Giggs, who played 64 times for his country, analysed Wales' win on ITV's highlights programme and said: "I'm so proud".
Coleman said he was quietly confident Wales could spring an upset and that they deserved the win.
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.
Although fans of Welsh football are still very much riding the crest of a wave, many have reacted to an article published by the Daily Mail this weekend, claiming that Welsh success in the tournament was down to English-born players.