Costa was already on a booking when he clattered Hammers keeper Adrian with a studs-up tackle during Chelsea’s 2-1 win at Stamford Bridge.
But referee Anthony Taylor took no action before the Spain striker went on to score the winner in Monday night’s London derby.
Noble said: “How long does it take? It probably takes about five seconds for someone upstairs to look at a video. And that works both ways then.
“I never blame the refs because I know how tough it is, how fast the play goes, how difficult it is to keep up with the play. But someone has got to give us some help.