The Chilean forward, 28, was confronted by team-mates on their return to the changing room and one of them had to be held back as tempers flared.
Sanchez was left out of the starting line-up at Anfield but came on in the second half as Arsenal lost 3-1.
Arsenal boss Arsene Wenger said it was a tactical decision to omit Sanchez.
Wenger brought on his top scorer at half-time, with his side 2-0 down, and he provided the pass for Danny Welbeck’s goal.
He has been directly involved in 26 goals in his 26 league games this season, scoring 17 and assisting nine.
However, Wenger said he had decided to start Welbeck and Oliver Giroud instead to provide a more direct attacking threat.
The defeat was the Gunners’ third in four league games and saw them drop out of the top four.