"It is disappointing to end the season without winning a single trophy. It is the first time since 2010 that we end the season without silverware," said Khoza.
"We disappointed the spiritual owners of the club [the supporters] who are used to celebrating winning trophies left, right and centre.
"The only consolation now is the African Champions League.
"We should have at least defended the Premiership. April was a bad month for us, where we drew seven games and gave away many points. We had no business losing games against Chippa United and Maritzburg United."
Pirates' management is also said to be unhappy that the technical staff are "on holiday" despite qualifying for the African Champions League group stages.
Pirates reassemble on June 18, a full month before their first Champions League group match against AC Leopards of DR Congo at Orlando Stadium.