Merseyside Police has launched an investigation following a host of "totally unacceptable" tweets directed at Everton duo Jordan Pickford and Richarlison.
The pair were both involved in high profile incidents in Saturday's derby which ended 2-2 at Goodison Park.
Pickford avoided a red but may have ended Virgil van Dijk's season with the Dutchman having to undergo surgery that could end his season.
Richarlison meanwhile was given his marching orders for a late challenge on Thiago that saw him leave the ground.
Nevertheless police have criticised the language used and insisted those responsible are "not beyond the law".
A Merseyside Police spokesperson said: "We are currently investigating a number of offensive Tweets made in relation to two Everton footballers.
"The language used in the Tweets is totally unacceptable and we are taking the reports extremely seriously.
"Those who use the internet to target others, and who commit criminal offences such as making threats or committing a hate crime in doing so, are not beyond the law.
"Detectives are making enquiries to identify the individuals who posted the Tweets and where we identify offences we will take action to bring those responsible to justice."
Tensions ran high during and after the contest with Liverpool denied a stoppage time win courtesy of a controversial VAR call.
The officiating system has been heavily criticised for its failure to adequately deal with Pickford's tackle on Van Dijk, who was given offside.
Many though feel as if the England goalkeeper should've been sent off.
Anger on the red half of Merseyside is only likely to increase after it was announced that Pickford would receive no retrospective punishment for his reckless tackle.
The on field referee, Michael Oliver, will also not face further action having seen the incident.
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