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."

The new P1 pupils will have teachers across the area seeing double when they begin the new term on Monday.
The new intake means there will be a total of 72 sets of twins at primary schools in Inverclyde.
Education officials were surprised when the number of twins rose to 16 in 2011. The huge increase since then has left them wondering if there is "something in the water".

Two men made off with a trolley full of alcohol from the supermarket in Annan at about 13:40 on Thursday.
About 40 minutes later a man matching the description of one of the thieves in the earlier incident struck at the Lockerbie Road store in Dumfries.
PC Carolyne Crozier said there were "clear similarities" between the thefts and asked witnesses to come forward.
Spirits worth more than Â£500 were taken in the first incident.
One of the men involved was in his late 40s, of medium build with dark hair with grey starting to show.
He was about 5ft 8in tall and was wearing a navy polo shirt with stripes across the front and jeans.
The second man was in his late 20s or early 30s, of slim build, quite tall with short, dark hair and was wearing Adidas three-stripe tracksuit bottoms and a hooded top.
In the Dumfries incident, a man was seen putting alcohol straight into a carrier bag. When stock was checked, it was found 10 bottles of vodka worth more than Â£400 had been taken.
The suspect was described as being tall and wearing Adidas striped tracksuit bottoms and an Adidas hooded top.
In a separate incident on the same day cashmere jumpers worth more than Â£600 were taken from The Canny Scots Shop at the Gretna Service Area between 10:00 and 12:30.
PC Crozier said: "There are clear similarities between the two Tesco thefts, right down to the description of one of the suspects.
"We are keeping an open mind as to whether or not the cashmere theft is linked."
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.
[NEXT_CONCEPT]
Schools in Inverclyde are preparing to welcome a record 19 sets of twins.
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Vodka and other spirits worth hundreds of pounds have been stolen from two Tesco stores in southern Scotland.