The Hammers did have opportunities to score throughout at Stamford Bridge but failed to convert and were eventually downed by a goal in either half from former West Ham man Frank Lampard and Eden Hazard, and Allardyce noted his side's lack of a cutting edge as a reason for their eventual defeat.
"I'm disappointed we haven't scored," the 58-year-old told the club's official website. "Chelsea is a very difficult place to come to and you have to maximise the opportunities you get.
"Matt Jarvis' service into the box today was really, really good and unfortunately we didn't have any goals on the end of that.
| PREMIER LEAGUE LATEST
|5/1||West Ham are 5/1 to finish in the top 10 with BetVictor
"He was our biggest threat today, every time we got him the ball today he skinned the full back. He put the ball where he should do, in the right areas with the right quality, but again the old Achilles heel for us of not scoring away from home has risen again.
"These kind of chances at Chelsea are difficult to come by, so when you do get them you have to punish the opposition and score them. At the moment we're not doing that."
However, though disappointed at his own side's performance, Allardyce was quick to praise Hazard, who lit up proceedings with an eye-catching display before scoring a superb solo goal to seal the three points for the home side.
"I will criticise my players if they deserve to be criticised, but you can't stop Eden Hazard, he's that good," Allardyce added.
"When he decides he wants to skip past players, with the ability he's got, he's good at kidding the defenders with what they think he's going to do. He doesn't do that, he throws them off balance and then skips past them again.
"He can finish, he's two-footed, he's quick, he plays really well in tight situations, so I thought it was a really hard job for us to handle him. They were a better side than us, but based on how much they've spent it's no wonder really.
"We tried to hang on, we had some opportunities, but if we don't keep a clean sheet away from home, we don't win - that's our Achilles heel."