Liverpool manager Brendan Rodgers admits he was "surprised and shocked" by the online racist abuse targeted at the club's striker Mario Balotelli.
Anti-discrimination body Kick It Out revealed on Thursday night that Italy international Balotelli had been subjected to more than 4,000 racist messages on social media this season.
Balotelli's Liverpool team-mate Daniel Sturridge and Arsenal striker Danny Welbeck have also each received more than a thousand discriminatory messages according to research carried out by Tempero, a social media management agency, and analytics firm Brandwatch.
Kick It Out estimates there have been 134,000 discriminatory posts this season with 39,000 of them directed towards Premier League players, and Rodgers says the issue must be addressed.
"I was aware of the findings and I was surprised and shocked," Rodgers said.
"I think one message is one too many to be honest. We support all the relevant organisations who are working to stamp all of this out.
"In the modern world and modern football it is something which is very much there, but we need to eradicate all of it out of social life and professional sport.
"I think it is the responsibility of us all to help all the various organisations stamp it out."
Liverpool goalkeeper Simon Mignolet takes a philosophical attitude to the online abuse of footballers and believes players must learn to handle the situation.
"I think that is normal in the world we live in," Mignolet said.
"Social media is something worldwide and you can't control it yourself really but you have to accept it.
"The spotlight is on you so you have to deal with those sort of things."
But Stoke manager Mark Hughes said he would welcome tougher sanctions against individuals who indulge in online abuse, believing they are safe behind the cloak of anonymity.
"The internet is difficult to police as we well know, but anything racist, homophobic - even just in general life - it should be rooted out and stamped on," Hughes said.
"It is not acceptable. The fact people can hide behind their computers on the internet makes it more difficult to manage and stop.
"But there needs to be a will and if there is a way of stopping this happening, then that should be encouraged."
More than 8,000 abusive messages were directed towards Balotelli, over half of which were racist. Welbeck received 1,700, of which half were racist, and Sturridge 1,600, of which 60 per cent were based on sexual orientation.
The sheer volume of racist and other abuse on social media has prompted Kick It Out to form an expert group to tackle football-related hate crime across social media, working with football, the main social media platforms, organisations dealing with internet safety and the police.
Kick It Out director Roisin Wood told Press Association Sport: "It is really shocking. We knew there was an issue but even we were shocked by how many the players have received.
"For one player to have received over 8,000 abusive messages is phenomenally awful.
"You cannot accept players getting that level of abuse so we want to bring this expert group together to see how we can address this.
"We don't see the problem going away. Some of the perpetrators are young people and they need educating that you cannot sit in your room and abuse people like this."
Kick It Out only started receiving complaints of social media abuse during the 2012-13 season and has since started reporting the incidents to True Vision - a national reporting facility which had been developed to deal with hate crime online.
The research showed the Premier League clubs receiving the highest volume of discriminatory posts were Chelsea (20,000), Liverpool (19,000), Arsenal (12,000), Manchester United (11,000) and Manchester City (11,000).
Twitter was the most common platform for abuse with 88 per cent of messages coming in the form of tweets.
West Ham manager Sam Allardyce believes more must be done to stop Internet trolls rather than just fine players who respond to the constant stream of online abuse.
In March, West Ham striker Carlton Cole was hit with a £20,000 fine after the 31-year-old admitted breaching social media rules by replying to a sarcastic post with an expletive comment.
Allardyce believes the companies behind the platforms should work harder to help reduce opportunities for abuse.
"They have a bigger responsibility than they are showing, particularly the fact that there is no need (for abuse) to be allowed," he said.
"Certainly with the amount of money they make they should block these guys. There is enough technology out there developed for them to say that 'we can identity a person, even if they hide themselves,' and then block them and ban them."
Allardyce - himself the subject of a parody Twitter account 'notBigSam', which has some 155,000 followers - can understand how players become embroiled in such angry exchanges.
"It is a fine line. I just don't put myself in that position to read it because I don't want to wind myself up by reading what is on that type of social media," he said.
"But that is one very difficult thing to sit and take if somebody is abusing you.
"It is difficult today because it is almost addictive, young people today very rarely have a conversation between themselves - even if they are sat opposite each other you will find that they are both on the phone not talking to each other, which is pretty sad, and that is going all the way down to young kids, eight or nine, sat with the phones now."
Allardyce added: "In football, we are adults and we need to try and deal with it better.
"For me, the scary bit is the amount of bullying that goes on via Twitter, Facebook, Google and Yahoo at teenage age at school where we have seen suicides because of it. That is where it needs to be stopped.
"These people should be identified and blocked from using that media network completely."