Marsh, a former Australia test batsman and coach, began a two-year contract Wednesday.
He told reporters he hoped to improve the current side after the retirement of match-winning players like Muttiah Muralitharan.
"Sri Lanka cricket is going through a phase exactly like Australia at the moment. Australia have lost a lot of good cricketers over the last two or three years, obviously Sri Lanka have lost some very good cricketers," Marsh said.
"I just see it as a great challenge. My goal is to take the team to another level, to work with all the younger players, take them and make them become better test cricketers, one-day cricketers and Twenty20 cricketers." Marsh said his plans included having a wider pool of about 30 players ready to play international cricket and emulating Australia and England in resting senior players ahead of bigger games.
"We've got to look at the bigger picture. There is a lot of cricket and sometimes we may have to rest a couple of senior players to make sure we can keep them going," he said. "This is what Australia and England do at the moment.
"One of the reasons England have become a very powerful side in world cricket is being organized in resting players and making sure the best players are ready to go in real big games," Marsh said.
Sri Lanka has been without a permanent coach since this year's World Cup when former coach Trevor Bayliss quit. Former Australia batsman Stuart Law, who was an assistant to Bayliss, was in charge for the tour of England from May to July. Rumesh Ratnayake, a former Sri Lankan seamer, was appointed interim coach for the home series against Australia in August.
Marsh, 52, has played 50 tests and 119 one-day internationals for Australia and coached the Australian and Zimbabwe teams. He has also been a selector for Australia.
He was in Sri Lanka earlier this month to watch his son Shaun play his debut test for Australia.
