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The pair had to be separated by the fourth official and Pulis was eventually sent to the stands by ref Jeff Winter. But McGhee has said that he will apologise to his opposite number.
"My dispute with Tony was handbags at dawn. I will apologise to him and I'm sure he will to me.
"You get excited during football matches and bigger managers than me have got into trouble, as we've seen recently.
Despite losing it on the touchlines, the Millwall manager was happy with the point that preserved The Lions' unbeaten start to their league campaign.
"Both teams could have won it," said McGhee. "But I thought a draw was a fair result."