Since Jayawardene stepped down from Test cricket in 2014 and Sangakkara followed him into retirement earlier this year the Sri Lankans have struggled.
On Monday they lost the opening Test against New Zealand after winning the toss and bowling first on a green wicket in Dunedin.
It was a harsh lesson for the new-look line-up with Kithuruwan Vithanage playing his ninth Test and Udara Jayasundera, Milinda Siriwardana, Kusal Mendis and Dushmantha Chameera having only nine Tests between them.
Skipper Mathews said that was a lot of experience to lose, but he believed the new brigade will develop into a quality side.
"They showed a lot of guts, they didn't want to give up even though one played his debut and others were playing their second or third game," he said after the match.
"The quality is there in the dressing room, it's just the mindset that needs to shift around.
"We've always talked about not having Sangakkara and Mahela in the team. It's history and we've just to move on with it, take responsibility and try and score runs."
Mathews lamented that his bowlers were unable to make the most of the favourable conditions.
"After winning the toss on a green wicket, I expected a lot more from the bowlers. We bowled a lot of loose stuff," he said.
In reply to New Zealand's first innings of 431, Sri Lanka were all out for 294.
New Zealand declared their second innings at 267 for 3 and Sri Lanka found the 405-run target too much as they folded for 282.
"Once the seam movement goes off in the first couple of sessions it gets really good for batting."
Mathews said he envisaged improvement, but it would take time.
"It's not easy for a batter to straight away come in and start performing," he said. "It's just a matter of time, hopefully they'll learn pretty quickly.