Blues midfielder Fabregas was involved in numerous on-pitch spats with Spurs players as tensions boiled over in the fixture that saw Leicester City secure the Premier League title ahead of Mauricio Pochettino's team.
The Spaniard is then claimed by the London Evening Standard to have sparked a mass brawl as the teams attempted to make their way back to the dressing rooms at full time.
Fabregas, a former Arsenal player, is said to have goaded members of Tottenham's coaching staff and jabbed at least one of them, sparking a 'furious response'.
And Roberts, famed for his hard-man approach as a player, took to Twitter on Tuesday morning to slam the 28-year-old, branding him a 'whinger' and a 'wimp'.
What a whinger fabregas was last night wish I was still playing would have loved to come up against him. What a wimp COYS— Graham Roberts (@GrahamRoberts4) 3 May 2016
"What a whinger Fabregas was last night wish I was still playing would have loved to come up against him", the 56-year-old wrote, adding: "What a wimp".
A feisty encounter saw a total of 12 players booked, of which a Premier League record of nine were from Tottenham, though somewhat remarkably both teams ended the game with 11 men.
The London Evening Standard reports Spurs will automatically receive a £25,000 fine, while a number of players are reportedly facing individual sanctions.