Mourinho managed Lampard when he was a player in two spells at Chelsea - between 2004-2007 and 2013-2015 - and the duo shared a close relationship.
“Sometimes as a manager, you can feel about a pundit, 'This guy has an agenda. This guy wants to attack me. This guy wants to protect the other one'. I don't think they don't feel that [instinct]," he told The Telegraph.
"I think they are professional in every aspect. But what I felt when I was a pundit, they also feel.
“Saying, for example, that I felt Frank should be a little bit more pragmatic in his approach [against Manchester United]... it hurts me.
"It is difficult to separate the professionalism of their [punditry] work with the human feeling that they have.
"I cannot blame some guy being pro-Liverpool if it is in his blood. I cannot criticise a guy being a little anti-Jose if he is not in love with Jose. You cannot separate the pundit from the man."