Klich bade Leeds an emotional farewell after stepping off the bench in Wednesday night's 2-2 home draw with fellow Premier League strugglers West Ham.
The hard-running 32-year-old, integral to Leeds' Premier League return under Marcelo Bielsa in 2020, is expected to join Wayne Rooney's DC United in Major League Soccer.
Marsch, wearing a farewell T-shirt in tribute to Klich in his post-match press conference, said: "Well we have enough quality in the team, but his personality, his courage, his bravado, you know that that part will be tough to replace.
"And I even said to the team, we have to find a way to find our inner Klichy in all of us to make sure that we're ready to perform in every match."
Marsch could not guarantee Klich game time following the arrivals last summer of Brenden Aaronson, Tyler Adams and Marc Roca and said the Poland international had opted for longer-term stability in MLS.
Klich revealed in a statement on Twitter late on Wednesday night that he had been reluctant to leave and that his four-and-a-half-year spell at Elland Road had "been a dream".
He said: "I wish I could stay, but I've never enjoyed being on the bench and I want to play as much as I can in the coming years and that is why I'm closing this chapter, but I will never forget my time in Yorkshire."
Fellow midfielder Adam Forshaw's absence against West Ham has raised concerns among Leeds fans over his fitness issues.
Forshaw has been dogged by injury during his time at Elland Road and underwent career-saving hip surgery in the US in 2020.
Marsch said: "We had a little procedure done with him (on Wednesday) that we think is a couple of days and then we'll see how he recovers.
"It's his hip that is causing him some issues. But we're hopeful that, it's like a little shot that can help loosen things up and hopefully help him with the pain."
West Ham halted a five-game losing run and the point against Leeds lifted them out of the bottom three on goal difference.
Under-pressure boss David Moyes paid tribute to joint-chairman David Gold, who died on Wednesday aged 86, and insisted he still had the London club's full support.
When asked if Gold had been a stabilising influence, Moyes said: "Yeah, but David Sullivan has been equally as good, if not better.
"I've been speaking to him regularly and he has been fantastic in his support and his backing.
"They have been really, really good and encouraging me and the team, want us to get back in form and move up the table, that's the plan.
"We've got a European campaign, we're set for that when we get to March.
"There are a lot of things that have happened in the last two-and-a-half years that probably give them the confidence to think they've got a manager they can trust and they can work with."