The sides drew 2-2 at Carrow Road on Saturday afternoon.
The Hammers found themselves 2-0 down with 76 minutes gone at Carrow Road, as goals from Robbie Brady and Wes Hoolahan looked set to give all three points to the home side.
However, a goal from Dimitri Payet on 74 minutes was quickly followed by the equaliser from Noble to hand his side what had looked like an unlikely point at one stage.
The result was arguably a positive one for the away team, but Noble says that there are a few players in the Hammers dressing room that are gutted not to have eventually scored all three points.
“The boys in there are probably gutted that we haven’t come away with all three points,” he told Sky Sports.
“[But] there’s times in the past were we would have just folded and gone on and probably lost the game but we showed our character.”
“The lads showed a lot of heart and should be proud.”
The good news for West Ham is that the result does not do too much damage to their hopes of qualifying for Europe this season.
With Southampton winning, they managed to move up ahead of the Hammers in the table, but Manchester United’s loss to Sunderland means they are still only a point away from fifth.
That leaves them very much in contention for a top six place, and they will hope to return to winning ways next time around to keep that push alive.