Cocu, also assistant of Bert van Marwijk at the national team, succeeded Fred Rutten who was sacked last month.
PSV started impressively and created five clear chances in the opening 20 minutes but Jeremain Lens missed the target twice and when he set up Dries Mertens the Belgian winger was denied by 'keeper Remko Pasveer.
Heracles, making their first Cup final appearance after beating AZ Alkmaar in the semis, never came close to a repeat of that form as PSV forged clear.
A long pass from Erik Pieters reached Mertens who headed the ball from 16 metres over Pasveer to double the lead after 56 minutes and soon afterwards a well-executed chip from Lens made it 3-0.
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