Australia declared their second innings on 439 for five during the lunch interval on the fourth day of the Test at Kensington Oval, and then restricted West Indies to 235 for three in their second innings when stumps were drawn.
Marshall has hit the top score so far in the West Indies innings of a career-best 85 before he was caught at short leg off Casson.
"I think the guys will have to come out positive and the first hour will be very important," Marshall said.
"We just have to stick in there for the first hour and take it from there. We always believe in ourselves."
For left-arm wrist spinner Casson, Marshall was his maiden Test wicket, and he too, looks forward to being part of a winning side.
"Anything can happen in cricket, but I certainly love being in our position," Casson said.
"A fifth day pitch is always going to be hard work. . .But we've got a lot of options, which is a fantastic position to be in. . .It's going to be a good Test for us, but we're up to it."
Marshall and Casson are the youngest members on their respective sides, and they each achieved memorable personal milestones.
Marshall's innings was his highest score in first-class cricket, and has eased concerns about his lack of experience, especially a first-class hundred.
"I'm not surprised with myself," he said. "I've been working hard for the past few months. It is paying off now.
"I've been training harder, talking to guys who have been playing for a long time. I am doing things that are right, things that will get me through.
"I go to training on time, try not to get out in the nets and bat like how I would play in the middle."
The scalp of Marshall was Casson's maiden Test wicket and he feels under no pressure, following in the wake of Shane Warne and Stuart MacGill as the first-choice spin bowler in the Australia side.
"I think we know that Shane Warne is a once-in-a-lifetime bowler and Stuey MacGill is not far behind," he said.
"There is always going to be pressure playing at this level. We have got a fantastic first-class set-up, and when you are not performing, there are other people to take your spot.
"I think it is up to each individual player. You have your own standards and you try to keep them, but I'll do the best I can and hope it will be good enough."
"But I will never be Shane Warne or Stuart MacGill. . .They are geniuses and I have no shame in saying this. I love watching them bowl, and I am trying to mimic them every time I play cricket.
"It's my goal to be as good as them, but if I do not get there, it will be a lot of fun trying."