The FA's disciplinary committee has scheduled a hearing on Wednesday to discuss the consequences of the events in Grozny.
Chechnya's strongman leader Ramzan Kadyrov, who serves as Terek's honorary president, called FIFA referee Mikhail Vilkov a "sellout" after he sent off Rizvan Utsyev late in the game and continued the criticism in what was meant to be an apology.
"I want to apologise to the entire football world for my remarks but not to the referee," the Kremlin-backed Kadyrov said in comments posted on the internet.
"It was a terrible game because the referee was biased. He did everything possible to change the outcome of the match - didn't award a (clear) penalty and gave Utsyev a second yellow."
Vilkov was also insulted by the stadium announcer, who called him a donkey over the loudspeaker.
Terek, who are in eighth place, could face a fine of up to 500,000 roubles (£10,700) or incur sanctions on their new stadium, named after Kadyrov's father Akhmat, who was killed in a bomb blast at the old ground in May 2004.
However, many Russian experts think Terek will only be forced to pay a small fine and Kadyrov is unlikely to face any sanction because the Kremlin does not want to destabilise the situation in the volatile North Caucasus region.
"It's a total disgrace to our game. If people at his (Kadyrov) level make such outrageous comments, then what should we expect from ordinary fans?" former player Valery Reingold, now a media expert, told the Sport-Express daily on Monday.
In November 2011, Terek were fined 500,000 roubles by the Russian FA after FC Krasnodar striker Spartak Gogniyev had his ribs and nose broken after being beaten by the club's reserve coach and administrator during a league game in Grozny.
The two Terek officials had been banned for 12 months each, while Gogniyev was handed a six-game ban and a fine for his involvement in the incident and was later released by his club.
The Russian FA's decision to ban Gogniyev was heavily criticised by the world players' union FIFPro, which described the outcome as a "disgrace".