Mourinho said the Real Madrid player's performance was "difficult to accept", saying Pepe was to blame to Germany's second goal and let his frustration boil over in getting sent off after confronting Thomas Mueller.
"Maybe it doesn't deserve a direct red card, but maybe deserves. Because in spite of not being a clear aggression, there is a body language that many, many times pushes the referees to have these kind of decisions.
"To leave a team playing with 10 men for such a long time is obviously a big handicap for the team.
The Chelsea manager also suggested that the Brazilian-born Pepe's naturalised Portuguese status should make him conduct himself better on the pitch.
"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 explained that Portugal’s 4-0 loss to Germany at the World Cup is just another in a line of disappointments for his home country.
Mourinho has cited previous tournaments where Portugal have done well until they have come up against a powerful side.
“If I go a bit back and I analyse the Portugal performances in the last appearances in World Cups and European Cups, Portugal doesn't get big results against the best teams," he said in his latest video you can watch above.
In the video he also gives his thoughts on Cristiano Ronaldo.
‘Jose Mourinho is an exclusive analyst for Yahoo’s worldwide football coverage, www.yahoo.co.uk/worldcup is the only place to read all his expert opinions during the FIFA World Cup 2014.’
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