Mourinho was dismissed in the final minutes for dissent, as he demanded a second booking for Felipe Melo.
"The referee's decision to send him off was an odd one and so Mourinho could not come to the Press area," said assistant manager Beppe Baresi.
"The referee was only whistling in one direction and booking our players, so we were right to get angry and I don't think we did anything that bad.
Zlatan Ibrahimovic struck both goals for Inter and Baresi continued: "We are happy with the great work rate of these players, the victories and the points we keep taking home. Considering the injury problems we deserved to win this tough game with real determination.
"The team cannot always do what it wants, as were tired and the defeat in Manchester certainly had an effect. We weren't as incisive upfront as usual, but we stayed very organised in defence."
Mourinho caused controversy this week when he stated "all of Italy will be happy that Inter are out of the Champions League" and also engaged in a public sniping match with Milan.
"Mourinho is a very cordial, good humoured person with the club and the squad," continued Baresi.
"When people try to throw stones and provoke him, then he does react. When he replies like that, it tends to be when he was provoked.
"I think many fans were disappointed, but the majority of Juventus and Milan supporters - even though they are Italian - took some pleasure from it."