The Hammers have moved three points clear of 18th place Aston Villa thanks to the surprise victory.
"It's massive," Antonio said. "There have been so many games where we've been so close, and today we've managed to get a goal which was taken away from us, we went 1-0 down but we got it back.
"It goes to 2-2 and then we get the winner in the end. It shows the grit we've got, the determination we've got and it shows that we're not going to give up and keep fighting to the end.
"VAR has gone against us a few times, but today it didn't stop us. We just kept going and got the victory.
"Tonight gives us that confidence, that belief. not the fact we've won the game but the fact we went behind, had a goal taken away from us, but managed to get back in.
"Chelsea are a quality team, they are fighting for the Champions League, so if we can do it against them we can do it against anybody."