Marsch inherited a struggling side from Elland Road favourite Marcelo Bielsa and has been unable to transform its fortunes, with Leeds in 18th because of an inferior goal difference compared with 17th-placed Burnley.
Everton secured its Premier League status with a dramatic 3-2 win over Crystal Palace on Friday (AEST), while Burnley took the lead but was held to a 1-1 draw by Aston Villa.
Leeds must better Burnley's result on Monday (AEST) to escape the drop but faces Thomas Frank's Brentford, which is unbeaten in its past 10 home league games against the Whites (W6 D4) since a 2-1 loss in 1950.
Marsch, speaking at a pre-match news conference, acknowledged the game with Brentford likely represents a must-win clash otherwise Leeds will be reliant on Burnley faltering against Newcastle United.
"[There were] lots of emotions watching it. We can learn a lot from how the other players can handle the pressure differently," he said of watching Friday's (AEST) Premier League games.
"We're excited for this challenge – we know we have to be at our best. I never came here to think it would be easy. I knew we'd have to fight for everything. I'll make sure we'll do this on Sunday [Monday AEST].
"It would have been a lot easier if we were locked into the league already, but the fact that we have to outpoint Burnley makes it very clear for us. A win gives us the best opportunity.
"I slept well last night because I still have confidence in our group. [It is] better when we control our fate, but that's not the case. [We need] to do whatever we can to get the points."
Marsch will be hoping to call upon Patrick Bamford, who has been out since mid-March with a foot injury, but is yet to make a final decision.
"More than anything, we're not risking him at any level," he said of his star striker. "At the moment I don't believe we would be able to.
"We will have one more meeting tomorrow with Patrick on what it looks like, what the loads have been, how he feels and then do a final assessment of is he available, how many minutes, what's the best strategy and then we have to be ready to let him go and play. That's where we are at."
Regardless of whether Leeds will be playing Championship football next campaign, Marsch plans to remain in charge.
"I'm still planning to be here even in relegation," the American added. "It's a long-term project and the club committed to me in that way. The connections we have made mesh well together.
"The support from everyone has been amazing, but I'm not thinking about the long-term project, only about Sunday and preparing for that."