The Magpies boss was sent to the stands for shoving Burt in the second half after claiming that the ball went out of play during a Spurs attack.
Hatem Ben Arfa's penalty gave Newcastle the win after Jermain Defoe had cancelled out Demba Ba's opener, but the triumph was soured somewhat by the actions of their manager.
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"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 was dismissed shortly after Ba had given Newcastle the lead and had to watch the remainder of the match from the stands.
He could now face a touchline ban or a fine from the Football Association as a result.