The club legend was relieved of his duties on Monday after 18 months into his three-year contract as the struggles in the Premier League proved decisive.
Mourinho who coached Lampard - won eight major titles during two separate stints with the Blues including the Premier League three times - suffered the same fate of being sacked by the club twice.
But the Tottenham boss feels it's not his place to reach out to Lampard during this period when asked about his feeling towards the news.
"I don't think Frank wants to speak to me or with anyone apart from his close circle of family and friends," Mourinho said after Spurs 4-1 FA Cup win over Wycombe.
"But I am always sad when a colleague loses his job and Frank is not just a colleague. He is an important person in my career so I feel sorry he did.
"But it is the brutality of football, especially modern football so when you become a manager you know that sooner or later it is going to happen to you."
Spurs are currently in fifth-place in the Premier League, four points ahead of ninth-placed Chelsea with a game in hand.