Liverpool were held to a 1-1 draw after their new signing Nunez was shown a straight red card just before the hour mark when he squared up with Andersen and appeared to head-butt the Danish defender.
The result leaves Liverpool winless after two games - down in 12th place - and fans vented their frustration by contacting Andersen on Instagram, where he highlighted the abusive messages he had received.
"Got maybe 3-400 of these messages last night. I understand you support a team but have some respect and stop (acting) tough online," Andersen said before sharing screenshots of abuse and death threats in his inbox.
"Hope Instagram and the Premier League do something about this," he added.
Reuters has contacted Instagram for comment.
Nunez's red card will result in a three-match ban and Liverpool boss Jurgen Klopp (55) - who is left facing a striker crisis with Roberto Firmino (30) and Diogo Jota (25) injured - said he hoped the Uruguayan would learn from his mistake.
Liverpool next travel to Manchester United on Monday the 22nd of August while Crystal Palace will host Aston Villa on Saturday the 20th.
