The game at Stamford Bridge ended in a 2-2 draw with a late Cesc Fabregas penalty ensuring that Slaven Bilic's side were not able to move into the top four of the Premier League.
And despite the highly controversial incident that led to the spot-kick being given - Ruben Loftus-Cheek appeared to trip himself up outside the box - Noble suggested that there are plenty of positives that can be taken from the game, especially when put alongside their performance in the FA Cup against Manchester United the previous week.
"To play the way we did against Chelsea, especially the first half, in the way we passed the ball plus the way we played at Old Trafford last week, just shows how far we have come," he told the London Evening Standard.
"It was enjoyable, nice to be involved with football like that. We play with Cheikhou Kouyate sitting there in midfield and then myself and Manuel Lanzini and Dimitri Payet linking up.
"Anyone who supports West Ham would have seen that game and been proud of the way we played."
While the Blues have not been the same side to the one that clinched the title last season, their league form under Guus Hiddink has been much more impressive, and so it was always going to be a difficult game for the Irons to come away with a victory.
However, had it not been for the penalty decision, then the result would have meant that Bilic's men would have gone above Manchester City and into the top four. And with City losing to Man United on Sunday, the Hammers would have gone into the international break in a Champions League qualification spot.
So while the initial reaction following the draw may have been one of dejection, the fact that the fans could have been disappointed with a point against the champions, and missing out on moving into the top four, highlights the progress that they have made in recent years.