The former Brazil manager did not say why he was standing down but made reference to pressures inside the club.
Corinthians are one of the biggest clubs in Brazil and the manager's job there is notorious as one of the most demanding.
"We got some players back to form over the season, we blooded some youngsters with promising futures and in addition to all that we qualified for the Libertadores," Menezes said after his team beat Criciuma 2-1.
"We did what we proposed doing at the start of the season and I feel like I’ve done my duty."
Corinthians will play a Libertadores qualifier against an as yet undecided club from Colombia and the winner will go into a group alongside holders San Lorenzo (Argentina), Danubio (Uruguay) and Sao Paulo.
(Reporting by Andrew Downie; Editing by Ian Ransom)
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