Goals from Jean-Phillipe Mateta secured the away win in the Premier League last time out for the Eagles, seeing them climb above United and into 11th spot.
However, that is now put on hold this weekend, as Palace, who have never won the FA Cup, travel to Yorkshire to face Doncaster.
This will be the first meeting between the sides in any competition since the 2018-19 FA Cup fifth round, with the Eagles winning 2-0 at the Keepmoat Stadium.
But, despite the gulf in league positions, Glasner is expecting a tough match.
"We prepare like we do for evey single game,” said Glasner during his pre-match press conference.
“We go there with respect and with the best available team”
Ben Chilwell signed for Crystal Palace on deadline day, moving on loan from Chelsea for the rest of the season.
The defender struggled for game time with the Blues after suffering a long-term injury and was surplus to requirements at Stamford Bridge throughout the season.
After training "really well", Glasner wants the full-back to make an instant impact, paving a way for him to feature against Doncaster.
The coach explained: "It was about who can help us immediately. We have three and a half months. He played wing back under Tuchel when they won the Champions League, he can play in a back four, many aspects worked for him.
"The plan is that Chilwell gets minutes at Doncaster."
Expectedly, Palace are set to rotate for the clash, but Glasner revealed that Adam Wharton could also be in contention for minutes.
Eberechi Eze will not feature due to injury, whilst Eddie Nketiah will also miss the game having twisted his ankle in training.
But, there was some hope for Matheus Franca, who has yet to play a single minute this season due to a persistent groin injury. Glasner added that the Brazilian is likely to be part of the squad for the FA Cup tie with a final decision on his inclusion due on Sunday.
The manager also added: "Adam Wharton looks very sharp in training, he looks very stable now. He is available."
Along with Chilwell's signing, much talk around Palace on deadline day was about Marc Guehi. The South London rejected a bid from Tottenham Hotspur north of the River Thames for a fee thought to be in excess of 70 million pounds, but the manager admitted replacing him so late in the window influenced their decision.
He added: "It was clear in our situation that we can't sell a player on deadline day as we can't find a replacement in a few hours."