Spain broke several passing records in their 4-0 win over the Republic of Ireland on Thursday night, including the highest number of passes in a European Championship match with 859 and an individual record for Xavi with 136.
Those statistics once again drew comparisons between Vicente del Bosque's side and Barcelona.
However, despite there being seven Barcelona players in the Spanish squad, Mourinho has defended the representation of players from his own club in the national team.
He told Marca: "They talk about the national team and Barcelona but there are also five players from Real Madrid.
"I don't understand why they mix them because they are two distinct things. Spain isn't Barcelona.
"Barcelona were the champions of Spain. And I repeat, were the champions because now they are not."
However, Mourinho does believe that Spain remain, along with Germany, the favorites to win the European Championships.
"Spain are the world champions and there is no doubt in this," said the Portuguese.
"They are one of the best teams in Europe and, if everything goes normally, Spain has to qualify, advance and compete, possibly with Germany and a couple of other teams, to be the champions of Europe."