The England international hit the post from the spot as United lost 2-1 at Old Trafford.
There had been controversy over who would take the next penalty for the Red Devils after Paul Pogba missed in the 1-1 draw at Wolves on Monday.
And Manchester United fans noticed Martial immediately handed the ball to Rashford making it clear he is now the designated man for spot kicks at the club.
The forward was unable to convert though as Palace stunned their opponents.
Much like Pogba, Rashford received racial abuse on social media following his miss.
United fans brought a banner to Old Trafford to show their support for the World Cup winner and that they are all against racism.
But that didn’t stop some on social media targeting Rashford as the Red Devils lost.
Chelsea’s Tammy Abraham and Yakou Meite of Reading also received abuse this week.
In a statement on Saturday, Kick It Out said: “The vile racist abuse on social media continued today.
“This problem will not go away and needs decisive action – that is what we will be making clear to Twitter when we meet.”
United boss Ole Gunnar Solskjaer believes his side should have had had more penalties awarded against Palace.
The Norwegian has also backed Rashford to bounce back and score the next penalty he takes.
He said: “There were a few other [penalties we should have been given], definitely. Fine margins, isn’t it?
“We’re disappointed of course that we didn’t win the game and I’m sure Marcus will look at his penalty again, but he’ll definitely step up again and score.”
United are next in action against Southampton in the Premier League on Saturday (12.30pm).