The Scots are preparing for friendly matches against Italy in Malta on Sunday and France in Metz on 4 June.
"We can definitely get to the World Cup," said the Cardiff keeper.
"We've got a good group of young lads coming through, so we don't see it [the Euro 2016 failure] as a last chance."
Gordon Strachan's men begin their World Cup qualifying campaign against Malta in September. Their qualifying group also contains England, Slovakia, Slovenia and Lithuania.
Marshall concedes it will be tougher to qualify for the World Cup than the Euros, but believes good showings in the upcoming friendlies can set them up for a successful campaign.
"It's only the top two in the group that proceed so it's going to be harder," said the 31-year-old, who should add to his 22 caps against Italy and France.
"We're going to come up against England in the qualifiers, so the higher level you play against benefits everybody.
"For the young lads coming in and getting that experience, it's going to be big games, big atmospheres, especially the France game over there.
"The better the team you play against, the harder the game, but it definitely benefits us in the long run.
"Obviously the disappointment was there from the Euros, but I think we can take a lot of belief and confidence from a lot of the games."
With Marshall's chief rivals for the Scotland goalkeeping jersey - Allan McGregor and Craig Gordon - absent from the squad, the former Celtic stopper feels it is a good opportunity for him to cement his place for the national side.
"I'm just looking to keep playing," he said. "I've got an opportunity now to probably play most of the two games because Craig and Allan have pulled out.
"Hopefully I can get the two games, do well again and keep my place."
David Marshall says Scotland's failure to make Euro 2016 was not their "last chance" to qualify for a major finals, insisting they can make it to the 2018 World Cup in Russia.