Carroll angrily stormed down the tunnel at the London Stadium after being overlooked when Moyes made a triple substitution with his side already 4-1 down.
Javier Hernandez, Joao Mario and Arthur Masuaku were all brought on ahead of the striker, who scored a 90th-minute equaliser off the bench against Stoke City in his first game back from injury earlier this month.
"It's something I'll deal with. In this situation what you need is everybody to be a team member so if he has done that, I'll look at it and I'll deal with it," Moyes is quoted as saying by the Evening Standard.
Sunday's result leaves West Ham 15th in the Premier League table, just three points clear of the relegation zone.