The Whites' 2-1 loss at the Emirates Stadium was compounded when they had skipper Luke Ayling sent-off with a three match ban now seeming certain to rule him out for the final three games at the same time as another senior player and right-back Stuart Dallas is out through injury.
The defeat also saw United drop into the bottom three with pressure now intensifying that they must get points from each of their remaining matches at home to Chelsea and Brighton then at Brentford on the final day of the season.
It is now out of Leeds' own hands whether they stay up or not, but Marsch publicly is not pressing the panic button.
He said: "We know we let ourselves down by the way we started.
"I have to find a way to be real with them but positive, recover and go again. Not feel sorry for ourselves. That's the only way I can deal with tough moments.
"I said before I had a singular focus on the next four games, now it's on the next three games. I do believe that (we can get out of it).
"I would just say we dug ourselves a massive hole and made a difficult task much much more difficult. Obviously far from the start that we wanted, but our resolve and our fight, when the game was incredibly hard, was amazing.
"A young keeper can make mistakes at times, it's how he responds and after that I thought he was quite good. We'll need him in the last three matches. We're down to not a lot of players. We need every guy to help us get through this situation.
"I know there's no rewards for coming away without points, especially now we're in the relegation zone but we have to stay positive, strong and we have to forge on. That's the only way we can operate right now. Our focus is fully on Chelsea right now, to do whatever we can to recover and prepare for another big match."
Marsch refused to have a go at Ayling for the red card he picked up for his rash challenge on Gabriel Martinelli.
He added: "It's a little bit ironic, given it's 500 matches for Luke and such an experienced player.
"A moment of poor judgement for him but he's been an incredible part of what we've accomplished so far since I've been here. I'm disappointed for him and the team, we just have to accept it and move forward.
"He apologised but it's not the time to point fingers. If we start playing the blame game with our team, we're screwed.
"The only potential we have to fight our way out is sticking together, being disciplined and believing in what we're doing. We have to push ourselves to be better."
With Burnley losing a day earlier the chance was there for Leeds to give themselves a huge boost in the relegation dogfight, but they never looked likely to take it after making a shocking start when just about anything that could go wrong did.
They were quickly behind when Illan Meslier made the kind or error that has sadly been coming as he took too long on the ball after it was passed back to him and the super sharp Eddie Nketiah raced into pounce with a pickpocketing toe poke past the Whites keeper from close range.
It was not as if Leeds did not know about Nketiah from his months on loan at Elland Road last season, but it was to his credit that his celebrations at scoring his opportunist goal were muted as a respect for the club he played for.
Nketiah doubled the pain on the Whites fives minutes later, however, with an impressive finish, although he had been given the freedom of the box to stroke home a low pull back.
With Gabriel Martinelli causing problems every time he had the ball down the left United were chasing shadows at times and the Gunners were full value for their early two-goal advantage and could have gone further in front with Meslier saving well to deny Bakary Saka.
It certainly did not then help when the visitors went down to 10 men as Ayling's reckless challenge on Martinelli led to him being sent-off after a VAR intervention following a yellow card dished out by referee Chris Kavanagh.
It was out of character for the stand-in skipper, but showed his frustration at the way his team had started the game perhaps.
Worse challenges have gone unpunished by red cards despite the VAR availability, but there is never any chance of a Leeds player getting away with any kind of two-footed challenge like this when others have been sent-off despite making contact with the ball in recent seasons.
It meant an early end to the game for Joe Gelhardt who had been chosen to start up front with Pascal Struijk coming on and a back five system now put into operation.
The fact that Leeds did not concede another goal was testament to the change in system working to some extent although there were a few close shaves, notably when Arsenal were wrongly given a free-kick of the edge of the box after Martinelli had been allowed to carry on despite being offside.
It led to Martin Odegaard's effort being deflected and only half-saved by Meslier before Diego Llorente produced an acrobatic clearance to prevent the ball from crossing the line.
Arsenal obviously dominated again in the second half with their extra man, but United stuck to their defensive task with a few let offs as Martinelli, Nketiah and Saka could not add to the home lead.
Unbelievably from their first corner of the game and their first shot Leeds pulled a goal back with Junior Firpo flicking on Phillips' flasg kick and Llorente coming in unmarked at the back post to volley home.
It raised hopes of an unlikely draw, but their only other effort came in added time as Firpo again flicked on a Phillips cross, but Rodrigo could not make strong enough contact on a second header and home keeper Aaron Ramsdale saved.
(Nketiah 5, 10)
Arsenal: Ramsdale; Soares, Holding, Gabriel, Tomiyasu; Xhaka, Elneny; Saka (Pepe 68), Odegaard, Martinelli (Smith-Rowe 78); Nketiah (Lacazette 90).
Leeds: Meslier; Ayling (sent-off 27), Koch, Llorente, Firpo; Phillips, Klich (Bate 45); Raphinha (Rodrigo 60), James, Harrison; Gelhardt (Struijk 29).
Referee: Chris Kavanagh