Leicester coach Richard Cockerill described Toulon prop Martin Castrogiovanni's five-minute rant as "petulant" and said it will "get him in hot water".
Ex-Tigers prop Castrogiovanni criticised Cockerill after Toulon's European Champions Cup loss on Sunday.
"He has no understanding of what it takes to run a rugby club," Cockerill said. "It is not for him to comment."
Toulon apologised to Leicester and said they will investigate the incident.
Defending European champions Toulon said they are also investigating former England player Delon Armitage over claims the full-back used offensive words in front of fans.
The French club added that they "will punish the players if deemed necessary" and "take the opportunity to offer its apologies to Leicester Tigers for the inconvenience caused".
Leicester icon Castrogiovanni was upset with the Tigers for claiming he left Welford Road in 2013 for a pay rise.
Using several swear words during his post-match outburst, he said: "Cockers talks about the money, but I paid £100,000 from my own pocket to leave this club because I want to play rugby."
Cockerill told BBC Sport: "The fee he paid was 100,000 euros (£79,000), which was reimbursed to him by Toulon.
"We have some very big-hitters on the board. To call them amateurs and to use the language that was used against the club and myself was inappropriate to say the very least, and untrue.
"We're the most successful English club of all time. It's a petulant outburst that will no doubt get him in hot water."