The Hammers are just three points clear of relegation with three games remaining this season and matches against Wigan, Fulham and Manchester City will determine their fate and that of their manager.
Zola has been under considerable pressure in recent months due to the club's poor form and public criticism from co-owner David Sullivan, and rumours continue to persist that the Italian will be leaving West Ham in the summer.
Portsmouth manager Avram Grant, former Manchester City boss Mark Hughes and Steve McClaren, currently managing FC Twente, have all been linked with the job, but Noble hopes Zola is not cast aside by the club.
"He's the manager so he will take the brunt of criticism but I think the criticism is unfair,'' Noble told the Telegraph. "He's dealt with the criticism unbelievably well. There have been six or seven games where we've been in the lead and given away silly, late goals. Sometimes it's concentration, sometimes it's bad luck.
"He's a lovely fella but when he needs to make a decision, it gets made. That's why he brought Steve Clarke in with him, because Clarkey is a strong character. If the manager wants to do something, he won't pussyfoot around. He's had a lot of criticism but you can tell the players are behind him, there's no rift in the camp.
"I want him to stay. He wants to play football the right way. He's still learning as a manager. He's still young. He's probably learnt more this year than he has over the past five years.''
West Ham have lost seven of their past nine Premier League games and remain vulnerable to an upturn in form from either Hull or Burnley, who sit below them in the table at present.
With relegation a real possibility, Noble has appealed to the club's fan base to remain supportive of the club in the final three games of the season.
"West Ham fans have always been unbelievable, but over the past month they've realised if they stick behind us it will help us," Noble said. "I know they pay their money and have a right to [criticise] but booing is going to make the team play worse. But they've been brilliant to us and will be again on Saturday.''