Sri Lanka recently appointed Mathews as Test and One Day Internationals captain while Dinesh Chandimal took charge of the Twenty20 team.
Sangakkara, who was in Bangalore on Saturday (February 23) to promote Sri Lanka tourism, spoke highly of all-rounder Mathews.
"It is a great challenge for the players. I have seen Angelo Mathews grow as a player, he is a leader and there is a lot more you can get out of him, he is a natural leader and then (Dinesh) Chandimal is young and for him it is important to gain exposure, build his image and slowly become the next leader after Angelo. I think it is a good combination but we need to give them patience and time," Sangakkara said.
On the subject of senior-junior transitions, he said: "I mean the term "senior" is quite an interesting term. You only get it when you have performed. If you don't perform you won't be in the side. The pressure to perform is there on everyone and it does not matter who the selectors are, you got to perform. And that's one thing that all of us know. I don't think anyone is given a place for the sake of a place. Whether they play a youngster, they got to take that position from a senior player and it is based on performance. Decisions in the future will be tough but I am sure they (selectors) know what they are doing."
On asked whether there was enough talent in Sri Lanka to replace big players like him, Tillakaratne Dilshan and Mahela Jayawardene, he said they had a "great stock of youngsters."
"I think you need the best younger players coming in all the time and at the same time you need the best performing players in your side as well. Performance ultimately is about winning or losing games and we have a great stock of younger players coming through and we are very, very happy that we play a big part in guiding them. At the same time, you are right our careers are coming to an end, sooner than later and by that time we should ensure that there are enough capable youngsters to keep on winning for Sri Lanka," he said.