United dominated possession as Jose Mourinho opted to pack the Chelsea midfield and although the overall performance pleased Moyes, his strikeforce of Robin van Persie, Wayne Rooney and Danny Welbeck rarely threatened.
"I thought we played well and I'm disappointed we didn't get a goal," Moyes said. "Maybe we lacked a bit of cutting edge with our final pass and final cross.
"I thought Chelsea defended well when they had to. If anybody shaded the best chances, it was certainly us. We went with three centre-forwards on the pitch and we wanted to try and win the game.
"We did everything we could and just lacked a ball to get Robin van Persie or Wayne Rooney the chance to score. 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."
Rooney came as close as anyone with a long-range effort that brought a decent save out of Petr Cech, while Welbeck screwed a shot wide and Tom Cleverley had a penalty appeal turned down after his shot crashed into Frank Lampard.
"If anybody created the chances it was us," the Scot added. "I picked an attacking team that was trying to score. We had boys who score goals and gave it a go.
"Maybe we lacked a real good pass through or a really top cross that might just have made the difference tonight or it might have been an individual moment of brilliance that we have seen in the past."