The Selecao opened up their World Cup campaign in disappointing fashion with a result that leaves them with plenty to do to make the knockout stages of the competition.
Their cause was not helped when Pepe was shown a red card for confronting Thomas Muller, and Chelsea boss Mourinho believes the Brazilian-born defender owes his adopted nation an apology.
"The fact that he's not even a Portuguese man, I think that should put even more pressure on him to behave in a certain way, which he didn't," Mourinho said.
"Maybe it doesn't deserve a direct red card, but deserves [punishment]. Because in spite of not being a clear aggression, there is a body language that many, many times pushes the referees to have these kinds of decisions.
"To leave a team playing with 10 men for such a long time is obviously a big handicap for the team."
Mourinho concedes the country of his birth are not one of the favourites for the World Cup, but he was still disappointed by their showing against Germany.
"If I go a bit back and I analyse the Portugal performances in the last appearances in World Cups and European Championships, Portugal doesn't get big results against the best teams," he said.
"If I go back to the last European Championships [Euro 2012], we lost against Spain on penalties. We also lost against Germany. In the last World Cup, we couldn't score against Spain and Brazil.
"So to say I expect Portugal to beat Germany or to expect Cristiano [Ronaldo] to score three or four goals like he does against other teams, I would be lying.
"At the same time, I was expecting a game that was much more balanced. I know the circumstances were difficult and playing with 10 men for such a long time, but 4-0 is disappointing."