The Hammers face promoted duo West Brom and Blackpool in back-to-back games as they aim to drag themselves off the foot of the Premier League table.
Avram Grant's side have managed just one win so far this season to prop up the table with seven points from their opening 11 games.
Noble had been one of the Hammers' best players during that difficult period, but is set to miss at least the next two home games after having his appendix removed last week.
The 23-year-old returned to light work at training this week and, after receiving the fan's Player of the Month award for October on Tuesday, reassured the club's loyal support that the players were doing their all to turn things around.
"We are all working hard as a team together," he said.
"The backing of the fans is important and they have been fantastic for us in every game this season.
"We want them to know we are all doing our best to turn results around so we can move up the table.
"Although I won't be able to play a part against West Brom and Blackpool this week, I will be like everyone else in supporting the lads."
West Ham showed signs that they could put their early-season problems behind them after claiming a 2-2 draw at Birmingham at the weekend.
Grant employed a three-pronged attack at St Andrews after recalling Carlton Cole to partner new arrivals Frederic Piquionne and Victor Obinna.
The attacking philosophy looked like it would pay immediate dividends when they stormed into a 2-0 lead thanks to goals from Piquionne and Valon Behrami, before the hosts battled back for a point.
While disappointed to miss out on a win, Noble thinks the Hammers showed they are capable of claiming some crucial points, starting against West Brom on Wednesday night, to lift them up the table before his return.
"If we can play like we have been doing lately, there is no reason why we can't pick up points in these games," he added on the club's official website.
"I am feeling fine after the operation. I have been resting up but I am now looking forward to getting back playing and I will be ready to do my bit for the team as soon as I can."