Marsch's side snapped a seven-game winless run by thrashing Cardiff 5-2 at Elland Road to seal a fourth-round tie at either Accrington or Boreham Wood.
A more pressing Premier League fixture at home against Brentford awaits Leeds on Sunday, but Marsch hit out at "awful" social media reports of player unrest in the dressing room.
Marsch said: "This report that comes out, the bull-**** about some of the players are against me is just awful. It's just awful. We are united. We are together.
"We are doing everything we can as a group, we are all harbouring the responsibility, especially me, and we believe in ourselves.
"We know we're going to get better and so we're certainly not done and we have a big challenge on Sunday, but we're going to keep going."
Willy Gnonto and Patrick Bamford both scored twice and Rodrigo fired his 12th goal of the season as Sky Bet Championship strugglers Cardiff were dismantled.
Callum Robinson headed a late consolation for Cardiff and converted a stoppage-time penalty after Marc Roca had handled, but Leeds' display helped ease some of the nerves on the terraces before Brentford's visit.
Leeds, two points above the bottom three after winning just two of their last 15 top-flight matches, have been boosted by the arrival of £36million club-record signing Georginio Rutter from Hoffenheim.
Bamford and Luis Sinisterra have also returned to action after injury and Marsch is hoping victory over Cardiff can prove to be a watershed moment.
He added: "We said two days ago, because Luis had his first day of training, Georgi had his first day of training, and we said at that point: 'Now we've got something'.
"I know it's hard for everybody to be patient. I know it is and obviously when we're not getting the points that we should be getting I come into the spotlight."
Cardiff interim manager Dean Whitehead endured a miserable first game in charge after the Welsh club sacked Mark Hudson last Saturday.
The Bluebirds face a relegation battle of their own after an eight-game winless run in the Championship, but Whitehead, who will be in charge for Saturday's home game against Millwall, took heart from Robinson's late double.
"To come back in the last five or 10 minutes and score two, I think we have to take positives from it. We have to take that into Saturday," he said.
"It's good to get Robbo (Callum Robinson) on the pitch. He hasn't trained much or played much in the last three weeks. So to get two goals, we'll take a positive going into the weekend."