The 26-year-old gave the hosts the lead from the penalty spot on after Hull goalkeeper Allan McGregor was sent off for a foul on Mohamed Diame but Nikica Jelavic equalised for the Tigers early in the second half.
West Ham struggled to assert themselves on their numerically disadvantaged visitors and, despite a James Chester own goal handing Sam Allardyce's men the three points, the home supporters were less than impressed and jeers were heard at the full-time whistle, with the manager cupping his ear in disbelief.
Noble, whose side sit 11th in the Premier League and nine points clear of the relegation zone, admitted that they were below par but urged fans to help them finish the season on a high, telling the club's official website: "Although it wasn't our best performance we did not fall short on effort and that has been a consistent theme during our recent upturn in form.
|WEST HAM LATEST
|12/1||West Ham are 12/1 with Bet365 to beat Sunderland 2-1|
"I know people will say I am biased but, on our day, we undoubtedly have the best fans in the country. On behalf of all of the players, I can say that your support really can make a difference."
Allardyce's position has come under scrutiny this season, particularly when the Hammers were in the bottom three and suffered a 5-0 loss to Championship side Nottingham Forest in the FA Cup before going down 6-0 against Manchester City in the Capital One Cup.
But Noble says that crowd unrest can affect the players' performances and wants to make Upton Park an uplifting environment.
"We will always perform better when we are feeling relaxed and comfortable - as you would in any job," he opined, "and I must admit the anxiety from the stands can spill onto the pitch and get into our minds, as much as we try to ignore it.
"When that happens, some players can be affected and they make mistakes that they would not normally make.
"I think you could see that in our performance [against Hull] as we made mistakes we would not normally make and didn't retain the ball as well as we have done in previous games.
"For that reason, I would ask that you to give your backing to the boys because I can tell you that we are giving 100 per cent for the shirt and 100% for West Ham.
"We know that you have spent your hard-earned money to watch us and we desperately want to put a show on for you in every game."