Mount wore the armband in Lampard’s last game as Chelsea head coach and the Englishman said he was impressed with his compatriot’s leadership quality.
Lampard has been widely criticized during his time at Stamford Bridge as people thought he used to favour Mount.
The former Derby County manager has revealed he didn’t know it was his last game in charge, and says the England international deserved to be trusted to lead the Blues and challenged him to "rise up" to the role.
"A nice feeling when I left Chelsea in my last game was that I made Mason captain," the Chelsea icon said at a QA at the Willow Foundation ahead of the London Football Awards.
"It wasn't a gesture because I didn't know I was leaving! But it was about his authority and standing in the group that had risen. He needed to see that and understand that. He needs to rise up.
"The minute I gave him the armband, I saw the look on his face and what it meant to him. That's something you get when you bring through academy players and fans love it. They have been fighting with desire since they were eight years old. That's tangible and something that's important.
"You won't always see it at 20 because they might have dips in confidence or moments in games that come. But when you have players who have that care, then it doesn't matter who the manager is. The desire they have themselves will carry though because they work so hard.
"When I left Chelsea, and this is no disrespect to the manager who has come in, but I would have put my house that they would think, 'Wow Mason Mount trains every day like a champion. He works off the ball and sets the press, has great quality, is improving all the time and now he is adding goals to his game.’
"That's the end of Mason Mount but as you can see, I like him a lot! I probably said enough about him because people used to say he was my son, but I'll be quiet there."
