Brentford player Ivan Toney and Rico Henry said members of their family were racially abused on Sunday at Goodison Park.
Toney and Henry played 90 minutes against Everton, as the Bees came from behind to win 3-2, with Henry scoring the winner in the second half.
After the game, they both tweeted that their families were racially abused.
Toney said he will do "everything I can to get you the punishment you deserve," while Henry said that seeing his mum "upset after being racially abused by a few Everton fans brought fire to my stomach".
In reply to Toney's tweet, Everton tweeted: "There is no place in football - or society - for racism.
"We are assisting Merseyside Police to ensure the individual is identified and dealt with appropriately."
In a club statement, Brentford said: "We are aware of an incident where racist abuse was directed towards family members of our players.
"A report has been made to both the police and to Everton FC.
"Brentford FC condemns all forms of discrimination and racist abuse in the strongest possible terms.
"We will offer our support to Rico's and Ivan's families and will fully co-operate with the investigation and any subsequent legal proceedings."
Toney tweeted just minutes before joking about fireworks let off outside the Brentford team hotel in the early hours of Sunday morning.
Merseyside Police said in a statement: "We are investigating reports that the families of two Brentford players were racially abused in Liverpool on Sunday.
"Allegations that a man directed racial abuse were made following the Premier League match between Everton and Brentford at Goodison Park."
Everton led through goals from Dominic Calvert-Lewin and Richarlison, either side of a Seamus Coleman own goal in the first half.
But Everton's Jarrard Branthwaite and Solomon Rondon saw red as goals from Yoane Wissa and Henry helped Brentford take home three points and keep the pressure on relegation-threatened Everton.