Hull goalkeeper Allan McGregor was sent off for bundling into Mo Diame in the area, with Noble tucking away the resulting penalty to put West Ham ahead at Upton Park.
But the visitors responded well and levelled through Nikica Jelavic early in the second half before a James Chester own goal proved enough to give the Hammers their first Barclays Premier League win in four matches.
Manager Sam Allardyce, who raised his hand to cup his ear as boos rang around the stadium at full-time, said after the 2-1 victory that he had never seen a team receive a negative response after winning what was a pivotal game.
Midfielder Noble wants to see the club fighting on a united front.
"I appreciate that we did not play our best football and that, at times, it wasn't pretty," he said.
"More than anyone, I am keen to get the ball down and play, but sometimes it just doesn't happen for you as a team and as individuals, no matter how hard you try.
"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. On behalf of all of the players, I can say that your support really can make a difference.
"We will always perform better when we are feeling relaxed and comfortable - as you would in any job - 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 last night 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 give your backing to the boys because I can tell you that we are giving 100 per cent for the shirt and 100 per cent for West Ham United."
Hull, who have injury concerns over McGregor after he spent the night in hospital having suffered kidney damage in the collision with Diame, have fallen below West Ham following the defeat.
Steve Harper came off the bench to take on glove duties and the club confirmed on Thursday that fellow goalkeeper Eldin Jakupovic has been recalled from a loan spell at Leyton Orient.
Hull captain Curtis Davies was left ruing a good performance that yielded no points but took solace from the fact the Hull fans have yet to show dissatisfaction at the players this year.
"You don't need to be at your best to win games. The main stat at the end of the day is three points," Davies said.
"We can get some plaudits for the way we played and get a pat on the back, that is good because we can take something into the Stoke game.
"It is tough to take but it is strange at this place [Upton Park] that they came away with a 2-1 win and got booed off the pitch. At least we aren't in that situation."