It has been revealed that Parmitano, who became the first Italian to take part in a spacewalk in July 2013, gave a talk to the Italian squad this week at the Casa Azzurri in Montpellier, the team's headquarters in France.
Parmitano, 39, stressed the importance of teamwork, motivation and preparation, something Conte had tried to get across to his players since he took the reins in 2014.
"I'm not a football expert but I am a fan of the national team," Parmitano said.
"Even we, astronauts, are a small team, we train in a rigorous manner and we wear a blue suit. Just like the players of the national team, we are aware that we represent Italy's image around the world."
Italy, runners-up at EURO 2012, arrived in France minus star players and with a squad that many believed to be the country's weakest in a long time.
While Conte's men produced a workmanlike display in their 2-0 triumph over Belgium in their Group E opener, Friday's win seals Italy's place in the knockout stage, prior to their final group stage fixture against Ireland on Thursday morning (AEST) in Lille.