Details of the exchange are yet to emerge but Livermore had to be prevented from reaching supporters seated behind the bench.
When asked about the incident, Pardew believes Livermore must have been retaliating to abuse.
"I don't think he would have gone into the crowd unless he was provoked because I know Jake," the Baggies manager told Sky Sports. "I don't know anything other than that."
An Andy Carroll brace was enough for the Hammers to secure a comeback win over a struggling Albion side.