The midfielder gave the hosts the lead from the spot on Wednesday after Hull goalkeeper Allan McGregor was sent off for a foul on Mohamed Diame, but Nikica Jelavic equalised for the visitors early in the second half.
West Ham struggled to assert themselves on their numerically disadvantaged visitors but a James Chester own goal handed Sam Allardyce's men the three points.
However, the home fans were less than impressed and jeers were heard at the full-time whistle, with manager Allardyce cupping his ear in disbelief.
Noble, whose side sit 11th in the Premier League and nine points clear of the relegation zone, admitted that West Ham were below par but urged supporters to help the London club finish the season on a high.
"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," he wrote in a message to fans on the club's official website.
"Our win at Cardiff, draw at Chelsea and the four wins in February were all secured with your fantastic backing.
"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 West Ham 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 League Cup.
But Noble suggested that negative feedback from the crowd can have a detrimental impact on the performance of the players and he pleaded with fans to make Upton Park a vibrant place to play football.
"We will always perform better when we are feeling relaxed and comfortable - as you would in any job," he said. "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 to 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.
"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."
