Former Northern Ireland boss Worthington has seen the Minstermen take just one point from three games since he replaced the sacked Gary Mills at the beginning of the month.
"It's a man's game and it looked like men against boys," Worthington said after his side's ninth league defeat of the season at Bootham Crescent left them one point above the relegation zone with seven games to play.
"People are paying their hard-earned money coming to support the team and what they got back was simply not good enough.
"If I said anything else, everybody would think I was off my rocker.
"I've been in the game long enough to know when I'm getting sold short and when players are not performing. It's a big test and it will be interesting to see who stands up to it."
Worthington, who steered Norwich to the Premier League in 2004, added: "We need self-belief and a willingness, which is probably at the top of the list, to keep York City in the league.
"A lot of players are out of contract in the summer and maybe it's easy for them to under-perform and walk away and not worry about where York City will be next season, but that's not good enough.
"They are getting paid by this club and by the supporters. They've got to repay that with results."