Pardew was sent to the stands when he shoved the official following Demba Ba's 54th-minute opener at the Sports Direct Arena.
"It was ridiculous really. I have to apologise publicly, I've been to see [the officials] already," he told ESPN.
"I've been telling my players this week to behave and have the Olympic spirit. I can only apologise. It was stupid. I don't know what I was thinking."
Pardew could now be hit with a fine or a ban from the Football Association.