Villas-Boas saw his side progress to the UEFA Europa League quarter-finals 2-1 on aggregate, despite losing the second leg 1-0 in Turin.
After the final whistle, Villas-Boas got into an angry exchange with the Torino bench, and subsequently expressed regret for his actions.
"I lost my head," he told Sport Mediaset.
"I got it completely wrong and I apologise for my behaviour.
"I was angry with the Torino team manager, but it was not the behaviour of a coach and I am sorry."
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