Despite leaving the pitch injured during Sunday's final against hosts France, Ronaldo made a contribution to his nation's victory by urging them on from the touchline.
The 31-year-old also said on social media that he was due to begin his holidays but there has yet to be any confirmation of the extent of the knee injury that saw him substituted early in Sunday's final. "We've let a big chance to be champions pass us by".
Former France worldwide Frank Leboeuf has criticised UEFA's decision to name Antoine Griezmann player of the tournament at Euro 2016 and feels Portugal defender Pepe deserved the award more than the Atletico Madrid forward.
Tens of thousands of people welcomed back the Portugal football team in Lisbon on Monday after the team won the European Championship, its first major trophy.
If tests confirm the injury Ronaldo will not recover in time for the final of the European Supercup, which is a rematch of the 2014 final against Europa League winners Sevilla, to be played on August 9 in the Norwegian city of Trondheim.
When Santos was appointed in September 2014, Portugal had suffered a dismal World Cup and lost their opening Euro 2016 qualifier at home to Albania.
However, Managing Madrid reports that the first tests by Portuguese doctors have suggested a partly-torn ACL, which could see the three-time Ballon d'Or victor ruled out until the latter stages of the year. "I do not agree with this choice", Leboeuf said. "He gave me strength and positive energy".