The 27-year-old is said to have been walking with his four-year-old girl Teigan outside of the KC Stadium when a couple of male fans shouted abuse at him.
The Republic of Ireland international, who left the Baggies for Hull in January this year, scored against his former club, as well as won a penalty, in Saturday's 2-0 win.
After the incident, Kayleah Long took to Twitter to say: "Think it disgusting how people can abuse some1 in front of their child! You should b ashamed!
"Our daughter is 4years old and cried as was worried for he dad! Thank god I wasn't there."
Long decided not to celebrate when he scored against West Brom at the weekend.