The United boss was angry with his side's performance in Saturday's FA Cup quarter-final against the Seagulls, despite a 2-0 win at Old Trafford seeing the hosts into the last four.
Shaw was involved in the move that saw Nemanja Matic set up Romelu Lukaku for the opener, the Serbia international then heading in an Ashley Young cross to wrap up victory.
Young replaced Shaw at the half-time break and Mourinho – who was heavily criticised following the midweek Champions League loss to Sevilla – did not hold back in his assessment of the former Southampton full-back.
"Luke – I cannot say much more," said the Portuguese, who has gone on record with his criticism of the 22-year-old England player before. "It is a relation with personality. It is a relation to trust, it is a relation to class.
"My reason [to withdraw Shaw] was we work on the pitch a certain kind of movements, the two full-backs need to be really aggressive and always in front to make space for Matic and Scott [McTominay] to play in front of the two central defenders.
"And I didn't have that with Luke or with Antonio Valencia. I didn't change both because it was too aggressive to do it and then I have only one more change to 90 minutes.
"And then if we go to extra-time I have the possibility of a fourth change. But to do 45 minutes with only one more change, I think that would have been too aggressive.
"But to try to improve our offensive football and be more aggressive I have to change one. I decided Luke because at least Antonio, defensively, was capable of some good positioning.
"Like in one of their more dangerous movements in the second half, [Jurgen] Locadia made a dangerous run inside Eric Bailly and Antonio is still capable of [defending] this.
"Luke, in the first half, every time they went in his corridor the cross was coming and a dangerous situation was coming, so I was not happy with the performance."
Shaw moved to United in 2014, but injuries and poor form have limited him to just 39 Premier League appearances.