The home side had the better of the limited chances on Moyes' debut at the Theatre of Dreams and the Scottish tactician admitted his players lacked a bit of bite in the final third.
"I thought we played well and I'm disappointed we didn't get a goal. Maybe we lacked a bit of cutting edge with our final pass and final cross," he told Sky Sports.
"I thought Chelsea defended well when they had to. If anybody shaded the best chances, it was certainly us.
"You can play football in many ways. There's nobody who says it has to be done one way. We went out there and tried to win but just couldn't find that final pass.
"It could do with getting cleared up with what is and what isn't a handball because the managers aren't really sure. It was a big call in a big game like this."