Michael Olise was hit by a bottle and the Millwall fans directed homophobic chants at his team-mate.
Olise was hit by a bottle thrown by the crowd in the second half of the FA Cup third round victory over Millwall.
Crystal Palace fans set off fireworks after a flare was thrown onto the pitch.
The Palace players were booed by some fans when they took a knee before the game.
Millwall have confirmed that they will launch an investigation after the match.
Millwall Football Club has a zero-tolerance policy against discrimination and will investigate any alleged abuse. The club policy is that any individual found guilty of discrimination is banned from the club for life.
Sky Sports contacted Palace and the Football Association.
Gary Rowett is the manager of Millwall and Patrick Vieira is the boss of Palace.
"I don't think either of the clubs want to see those moments off the pitch but I am sure both will deal with those situations effectively," Rowett said.
"Discrimination is not something we want to see on the field and we are against it as a football club," said Vieira.
The Den was the site of a 2-1 victory for Palace.
This isn't the first time that Gallagher has been subjected to homophobic chanting. The fans chanted the same song at the same time as they beat Palace in the premier league.
Edleen John, the FA's Equality, Inclusion and Diversity Director, told Sky Sports News in August that there is a determination to drive the rent boy slur out of the game and that it should be comparable to racist abuse.
The Eagles scored two goals in the second half to win the game and progress to the next round of the FA Cup.