Suarez has apologised for his "inexcusable behaviour" after the incident during the 2-2 draw at Anfield on Sunday that has left the Uruguay international facing the prospect of a lengthy ban.
It is the latest in a series of unsavoury incidents in Suarez's career and PFA chief executive Gordon Taylor said the players' union would offer the striker help to deal with his temper.
Taylor told Press Association Sport: "There is no doubting his football ability, that's why it is so disappointing and embarrassing when he lets himself down. We have to work hard on anger management now. We have trained counsellors in this field and we will be offering their services to Liverpool and the player to try to improve matters."
The FA is reviewing the incident and Suarez is likely to be charged on Monday. Suarez is also one of the candidates for the PFA Player of the Year award to be announced on Sunday, and Taylor confirmed that the latest controversy would not affect his position on the shortlist.
Taylor added: "It's decided on votes and it is a football matter but of course it is embarrassing that it should happen."
Liverpool's managing director Ian Ayre cancelled a scheduled flight to Australia, where he was due to promote the club's pre-season tour, to deal with the fall-out of the Suarez controversy having learned lessons from previous public relations disasters.
He described Suarez's behaviour as "not befitting of any player wearing a Liverpool shirt" and said he would be dealt with internally - most likely by way of a heavy fine. Liverpool have stopped short of imposing their own ban on the striker but he is likely to be ruled out for the remainder of the season once the FA's disciplinary process kicks in.
Reds manager Brendan Rodgers said: "Having reviewed the video footage and spoken to Luis, his behaviour is unacceptable and I have made him aware of this."
The player issued his own apology - something he failed to do adequately when found guilty of racially abusing Manchester United's Patrice Evra last season - first on Twitter and then via an official club statement.
"I am deeply sorry for my inexcusable behaviour earlier today during our match against Chelsea," he said. "I have issued an apology and have tried to contact Branislav Ivanovic to speak to him personally. I apologise also to my manager, playing colleagues and everyone at Liverpool Football Club for letting them down."