Lampard was dismissed after overseeing a slump in form which sent Chelsea tumbling to ninth in the Premier League table. He is expected to be replaced by the German former PSG manager Thomas Tuchel, whose appointment could be announced on Tuesday.
Mourinho twice had spells as Chelsea manager which ended in acrimonious circumstances between him the club hierarchy.
He said: "I am always sad when a colleague loses his job. Frank is not just a colleague, he is an important person in my career, so I feel sorry he did (get sacked).
"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."
Mourinho was speaking after Tottenham's late show saw them beat Wycombe 4-1 in the FA Cup fourth round.
Spurs looked like being taken to extra time by the Championship strugglers as they missed a host of chances to kill the game after Gareth Bale's goal had cancelled out Fred Onyedinma's surprise opener for Wycombe.
Even the introduction of Harry Kane and Son Heung-min could not do the trick until the final five minutes when a Harry Winks strike and a quickfire Tanguy Ndombele double sent Mourinho's men through to a fifth-round tie at Everton.
The late goals were a blessing for Mourinho, whose side are back in Premier League action on Thursday when champions Liverpool visit north London.
"I knew that the game was going to be difficult - we started preparing for the game by showing the players what they did a few years ago at White Hart Lane," Mourinho said, referencing the 2017 fourth-round tie which Spurs won 4-3 at the death.
"Six of these players and the manager are still in this team.
"So that I think was a good start and then we prepared for the game knowing it could be hard and it was. It's not easy to handle their style of play.
"If you don't score goals they stay in the game and it was great for us to score in minute 85 because that gave us the possibility of not playing extra time, which would have been not good for us."
The game would have been a different story had Bale been more clinical in front of goal, as he missed several chances to add more goals to his tally.
But it was still a noteworthy night for the Wales international as he completed the first 90 minutes of his second spell at the club on his first appearance since 23 December.
"It was good, was good," Mourinho said. "Some good movement. Some one against one, beating people, attacking people, creating chances. Of course scoring a goal.
"Apart from that I never felt he couldn't play the 90 minutes. I never felt that I needed to change him and that is good. Of course the Championship is a good, competitive level and the aggression is high and the intensity is good. So I'm happy.
"We had some good performances from the boys that started the game. Of course Winks man of the match which is very much deserved because I thought he was very, very good in everything he did, apart from the goal.
"The goal is just a very small important detail but happy because I think the attitude of the team was very professional and it's the kind of game that even if we lose because we don't take chances and they score in the last minutes, let's say that, I wouldn't be sad because of the very professional performance."
For Wycombe the dream of a shock was a realistic one for 85 minutes as they held Spurs. But, in their first game back after a Covid outbreak, Gareth Ainsworth's men ran out of steam.
"I am a little bit deflated," the Wycombe boss said. "It was a tough last five minutes which reflects the scoreline, the other 85 minutes reflects a 2-1 scoreline. It was tough on the players.
"We have only trained one day in the last eight days because of Covid and the snow yesterday. I am proud of them."
When not managing Wycombe, Ainsworth sings in the rock band The Cold Blooded Hearts and he says Mourinho will always be welcome to collaborate.
"Absolutely - he said he might not be able to sing but I bet he can play a mean tambourine," he said. "He is a top guy and a great manager. He has given me a lot of respect tonight and I am humbled to be on the same touchline as him today."
Additional reporting by PA
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