The Hammers dominated for long periods at Stamford Bridge but failed to test Chelsea goalkeeper Eduoard Mendy in the absence of injured talisman Antonio.
Antonio’s replacement, Sebastien Haller, did not have a shot, while Moyes did not include a striker on his nine-man bench, which did include two goalkeepers.
Antonio has already missed seven League matches this season with hamstring trouble and Moyes suggested he may have to find another forward in his squad if the 30-year-old cannot get fit.
Asked if the Hammers were targeting a striker in the January transfer window, Moyes said: “I hope I get Micky back soon.
“If we don’t then we need to think what else we can do, how else we can do it. We need alternatives and options, we’re a little bit limited with that.
“If not then I’m going to have to start looking in my own group to find another Marko Arnautović or Micky Antonio. That’s what I’m going to have to try to do.
“We did a lot of good things but not enough good things in either box where it mattered,” he added.
“We’ve shown we can compete, we’re just lacking a little bit at both end of the pitch that would make the difference.”
At the final whistle, Moyes remonstrated with referee Chris Kavanagh and his officials as they left the pitch, and afterwards admitted he was unhappy with the standard of decision-making.
Jarrod Bowen had a goal ruled out for an apparent shove on Silva, while Declan Rice also saw a strike chalked off for offside.
“I just thought it was a poor level tonight,” said Moyes. “A lot of things didn’t go in our favour tonight.”
Asked directly if he was unhaopy at the decision for Bowen’s disallowed goal, he said: “I don’t know, I just thought the level wasn’t good. Any small decisions tonight or if there was any decisions that could go either way they certainly didn’t go in our favour. ”