The 23-year-old, who is the son of former Southend midfielder Andy Ansah, had been on trial with the League One club, and played 45 minutes of their pre-season clash with Partick Thistle last weekend.
The former Arsenal youngster also lined up against Ipswich Town last Wednesday, but was not included in the squad to take on Braintree Town on Saturday, and Brown has revealed that Ansah has now departed following an unsuccessful trial.
"Zak was finding it very difficult on the physical front and he's no longer at the football club," Brown told the Southend Echo. "But we wish him well on his search for a new club."
Ansah, who represented England at Under-16 and Under-17 level, has previously played for Charlton Athletic, Plymouth Argyle, Newport County and Woking.