Captain Matthew Upson has called for the players to unite and put in a concerted effort to get out of trouble.
"We need to have a long, hard look and change something about what we are doing," he said.
With seven Premier League matches to go, West Ham are one place and three points ahead of Burnley and Hull, in 18th and 19th place respectively.
Their relegation rivals have arguably an easier run-in while Hull also have a game in hand.
Sullivan has said West Ham, which had debts of £110m when he took over with Gold, faces "Armageddon" if they are relegated.
Reaching for his calculator, he told BBC Sport: "We have to remember there is over 15% of the season left - 18.42%, in fact.
"We will see. The bookies think we are going to stay up and they are normally right."
Zola's team were second best throughout against Wolves, with a Scott Parker shot that hit the post in the first half and a late consolation goal from Guillermo Franco among few bright moments in a dismal display.
Kevin Doyle, Ronald Zubar and Matthew Jarvis all got on the scoresheet for Wolves as they rose to 15th spot.
West Ham now face Stoke at home on Saturday but must also travel to Liverpool, Everton and Fulham before the end of the season.
Former Chelsea star Zola said he did not welcome fans jeering his players.
"It hurts me very much," he said. "I have a close bond with this team. The only way we can do better is to play better and win games. That's the only way we can react to this.
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