Gareth Bale says Wales "can have no regrets" after a 2-0 loss to Portugal in the Euro 2016 semi-final ended their hopes of a first major tournament win.
Two goals in three second-half minutes sealed their fate in Lyon.
"We have to be proud of ourselves," the forward said. "We have given everything on the pitch and off the pitch and tried to enjoy the experience."
Prime Minister David Cameron said Wales had "inspired a nation and made Britain proud" with their exploits in France.
First Minister of Wales Carwyn Jones said he was "sad it's over" but "very proud again".
Chris Coleman's side upset the odds to reach the last four as the likes of England, Italy, Spain and Croatia were knocked out in earlier rounds.
But he admitted: "It hurts that we lost. The players are gutted, but they need to look back and see they have done their country proud."
Reaching the semi-finals was a historic moment for Wales.
Their previous best tournament result came in 1958, when they reached the quarter-finals of the World Cup in their last appearance at a major finals.
After a goalless first half, Cristiano Ronaldo broke the deadlock on 50 minutes with a magnificent header.
Three minutes later, his shot was diverted past Wayne Hennessey in the Wales goal by former Manchester United team-mate Nani.
'A beautiful dream'
Wales began the tournament as one of the outsiders but caused a shock by topping Group B, finishing above England despite losing to their neighbours.
They then edged past Northern Ireland in the last 16 before upsetting a highly regarded Belgium side 3-1 in the last eight.
Their exploits earned rave reviews back home, securing a good luck message from the Prince of Wales before Wednesday's game against Portugal.
Footballers past and present, politicians, celebrities and other sportsmen and women were also full of praise for the Wales team.
Welsh rock band The Manic Street Preachers, who performed the country's Euro anthem Together Stronger, tweeted that the campaign had been "a beautiful dream" and thanked the team from "the bottom of our hearts".
Former Wales midfielder and BBC pundit Robbie Savage said: "The boys have made us all so proud of our country," while Wales rugby union wing George North tweeted: "Gutted but what an unbelievable tournament!"
Boxer Enzo Maccarinelli said Wales had achieved more than anyone thought possible, while cyclist Geraint Thomas, busy riding in the Tour de France, said: "The dream is over... but the boys have done themselves and Wales proud!"
Five months before Coleman was appointed in 2012, Wales were ranked 117th in the world. They reached a high of eighth in October last year, one month after moving above for England for the first time ever.
Wales were 26th before the tournament began but when Fifa updates its list on 14 July, they are set to rise to 11th - above England again.
'An amazing journey'
Wales players had started referring to their fans as 'The Red Wall'.
"We want to thank the fans for all the support we have had, they have been absolutely incredible," Bale said. "I felt we deserved better.
"We wish we could have done it for them and we'd like to thank all the fans at home and all the ones who have travelled out and behaved themselves.
"It is difficult to analyse now as we are obviously massively disappointed.
"We tried our hardest to get back in the game, we fought until the last second and we are sorry we couldn't get to the final, but we gave it everything.
"It's been an amazing journey. We look forward to the future."
Coleman admitted a real sense of hurt but was proud of the performance.
"I have a dressing room full of disappointment unfortunately," he said.
"As much as I've told them that they should be proud of themselves, the nation is proud of them, they're still devastated.
"That speaks volumes for them and they'll get stronger from this experience.
"I always thought that whenever the time was to bow out it would hurt, but I didn't expect it to hurt this much. It was just one too far for us tonight."
'The shining star'
Bale and Real Madrid team-mate Ronaldo shared a warm embrace at the final whistle.
Asked what he had said to Bale, Ronaldo replied: "I congratulated him on their run. They were the shining star, the revelation of the tournament."
Ronaldo is now hopeful of winning a major trophy with his country, 12 years after they were stunned by Greece in the final of Euro 2004 on home soil.
"I've always dreamed of winning something with my country and it's just one step away," he said. "Dreaming is free so let's keep dreaming."
'It's not the end'
Coleman believes the performances of the squad in France have set the tone for the future.
"It's not the end of this group," he said. "There's plenty of football left in them."
Bale also believes Euro 2016 can act as a spur for Wales as they turn their attentions to qualifying for the 2018 World Cup in Russia. Wales open their campaign at home to Moldova on 5 September.
"We've got confidence now for the future," he said.
"We're all going to be disappointed now but we're going to pick ourselves up, dust ourselves down and we'll go again for the World Cup qualifiers."