Prime Minister Edi Rama told CNN in an exclusive interview that the players had been "the best ambassadors" for the country and deserved the reward -- a seven-figure bonus and diplomatic passports -- after their heroics at the European Championship finals in France.
Less than 24 hours after the country's first victory at a major international tournament -- a 1-0 win over Romania
-- he says the Albanian government has gifted €1 million ($1.13 million) to the nation's football federation.
Yet it is the awarding of the passports, he says, which shows the real magnitude of the team's achievement.
"The giving of the diplomatic passports is the most heartfelt and symbolic," Rama told CNN in a telephone interview late Monday. "Ambassadors have these passports and they are like ambassadors because of how they've represented our country.
"In terms of the team, they have made the most outstanding case of playing football in Europe and Albania."
Written off by many experts before Euro 2016 had even started, two defeats in two games threatened to flatten Albanian excitement at reaching its first top-level tournament. Now, depending on results in other groups, it could qualify for the last 16 as one of the best third-placed sides in the competition.
And, in a championship so far marred by crowd trouble, Rama has been impressed by the behavior of Albania's traveling fans.
"I don't think it's only the team who has done us proud -- the supporters have done too. When you read the headlines in the French newspapers saying 'God bless Albania' and 'Albania, you're always welcome back' it means a lot."
The Balkan state hopes to one day join the European Union, and Rama joked that he would like to see Albania play England -- which, as part of Britain, will exit the EU if its people vote to leave in a referendum on Thursday, though that can't now happen given the way the draw for the knockout stages is working out.
Albania has come a long way since the end of the 1980s when -- under the totalitarian regime of Enver Hoxha
-- it was one of the world's most isolated states.
No one was allowed to travel outside the country, and thousands were held in secret gulags. Beards were banned, as were the religions they were thought to represent.
Decades later, an estimated 20,000 Albanian fans were dancing for joy in Lyon on Sunday as a bearded striker, Armando Sadiku, scored the winning goal against Romania.
They also celebrated in the streets of Albania's capital Tirana, as well as in Pristina, Kosovo and across the Albanian diaspora.
Rama says the example set by the supporters has helped to shatter stereotypes which were held by those who still remember Hoxha's regime.
Albania is not expected to join the EU until 2020 but received candidate status in 2014, and Rama believes the success of the country's footballers is helping reshape people's view of the nation.
"I don't think there's a mechanical connection between the footballers and joining the EU, but there is certainly an inspirational one," he says.
"The players and the supporters have helped because some had a gloomy perception of Albania because we have suffered from heavy stereotyping."
Ten members of Albania's squad were either born in Switzerland or grew up there, with seven of them having represented Switzerland at Under-21 level before choosing to play for Albania -- a statistic that arguably signals the nation's troubled past.
Unfortunate against both Switzerland and host nation France, Albania produced a fine display to defeat Romania for the first time since 1948.
"The win a was a relief because in the previous games we deserved more," Rami says.
"It was a real curse, and there was a lot of tension in the final minutes against Romania because we thought the curse might come back.
"Now it is out of our hands and we must wait."