Parker said he was willing to fight through the pain for the initial date but took the opportunity to address it when the fight was delayed.
Junior Fa's trainer said his team is stuck in "The Higgins Show" with the fight now rescheduled for next year.
The 35-year-old is currently a free agent after the Toronto Wolfpack failed to be re-admitted to the Super League.
City Kickboxing trainer Eugene Bareman said it was Fa's turn to be in the limelight with his fight against Joseph Parker coming up.
US boxing promoter Bob Arum is considering Eden Park as a possible venue for the highly anticipated rematch.