Martinez escaped with just a yellow card despite going in with a high boot on Palmer, the Argentine seemingly being saved by the fact that his studs did not make a clean connection with the Chelsea attacker's upper leg.
By that point, Chelsea had only used three of their five permitted substitutions, but Palmer saw out the full 90 minutes at Old Trafford, where a stunning Moises Caicedo volley cancelled out Bruno Fernandes's penalty.
Maresca was quizzed on Palmer's condition after the game, and he revealed that the ex-Manchester City man required ice on his wound after Martinez's challenge, but he is optimistic that it is nothing serious.
"Hopefully he is okay. He has ice on it now," Maresca said at his post-game press conference, while also suggesting that he felt Martinez should have been dismissed for the challenge.
Maresca makes Martinez red card claim after Gary Neville comments
"I don't think he has the intention of going for the ball. For me, it is clear," the Chelsea manager replied when asked if a yellow card was too soft a punishment.
Maresca's sentiment was echoed by former Manchester United defender Gary Neville on Sky Sports, who suggested that Martinez was fortunate not to have been made to take the walk of shame.
"When you go that high I think you're asking for a red card. I think he's lucky. When you go knee-high and the ball's gone, I think it's a red," Neville said, before Roy Keane agreed with his view.
"He won't be happy with Palmer making a fool of him. It's a nasty challenge. But he doesn't catch him properly. It's down the side of his leg. If he had got sent off there would have been no complaints," Keane said.
Despite not contributing a goal or assist at Old Trafford, Palmer was still influential in the final third, making three key passes and winning nine of his 10 ground duels in Sunday's stalemate.
Palmer to miss next Chelsea game after Martinez tackle
As Palmer was able to see out the full 90 minutes on Sunday, it can be assumed that the blow he sustained from Martinez's foot is not overly severe, and he ought to be fine to return next weekend.
The 22-year-old will be given an extended break this week, as he was not called up to Chelsea's Europa Conference League squad and will therefore miss Thursday's clash with Armenian side Noah.
Instead, Maresca will be expected to hand opportunities to the likes of Joao Felix, Christopher Nkunku and Mykhaylo Mudryk in the final third, continuing his theme of making wholesale changes in the third-tier competition.
Palmer will be expected to make a swift recovery in time for next Sunday's crunch clash with Arsenal, whom Chelsea have now leapfrogged in the Premier League table on goal difference.