Hammers forward Marko Arnautovic netted a fine early goal to put his side in front at the London Stadium.
And David Moyes’ men held on to claim a vital three points.
Chelsea defender Cahill said: “We were well off it, we allowed them to get the early goal, we have been tight at the back recently and that was a poor one to concede.
“We just didn’t play our stuff. It’s frustrating. We were just not at the races – for whatever reason that is. It’s disappointing to come off and feel like that.
“I’m not one to make excuses. We do have loads of games – but if we played to our levels today we get something out of the game. But we didn’t.
“West Ham of course deserve credit, but we didn’t create as much as we can do.
“This was a huge game for us. We needed to win this game. We have to reflect and try and freshen up.”
Arnautovic’s goal was his first for West Ham following his mega-money move from Stoke over the summer.
He said: “I can’t describe my feelings, it was amazing.
“All the players what they did was amazing and we deserve the three points.
“The last few weeks we have put in a lot of work but we were not always lucky. I think it is come back and the confidence is going to be high now.
“We beat one of the top teams. Now we have to look to go up the table.
“It means a lot to me [to score]. I think to give something back to the fans and to the club.
“I was not in an easy situation when I came because of all these things that happen like the red card and illness but the last month I did quite OK. I want to score as many as I can now.
“We are working hard but we need to keep up the level.”