With the Manchester giants showing fluctuating form, their London rivals are taking full advantage. Tottenham are in second after drawing 1-1 at home to third-place Chelsea in a diverting match that saw Fernando Torres sent off for the visitors.
"I'm concerned after today's result, but only because we didn't play well," said Moyes, whose team took another blow six days after losing 4-1 to City in the derby. "But there are a lot of games to go and I'll try to put it right.
"It's not from the lack of trying or lack of forward players ... It's just not quite opening teams up the way we would like ... We missed that spark."
Even promoted teams Cardiff and Hull are above United after six games. Cardiff won their first away match of the season, 2-1 at Fulham, and Hull edged West Ham 1-0.
But another newcomer, Crystal Palace, lost 0-2 at Southampton, who are adding to the surprise factor this season by sitting in fourth.
Sunderland are bottom on one point before today's game against Liverpool. Unbeaten Everton host Newcastle tomorrow.
Arsenal midfielder Aaron Ramsey maintained his stunning start to the season by setting up Serge Gnabry's opener in the 58th then scoring himself four minutes later at Liberty Stadium. Ben Davies cut the deficit in the 81st but Arsenal held on and are confounding expectations.
West Brom fully deserved their first win at United in 35 years, with Saido Berahino clinching victory with a 67th-minute strike.
Wayne Rooney's free-kick score cancelled out Morgan Amalfitano's stylish solo goal, but a United side missing several regular first-team stars with a Champions League match at Shakhtar Donetsk in mind struggled throughout. Moyes' team have not scored from open play since the first day of the season.
City were toasting derby glory last weekend, but were brought to earth by the loss at Villa to drop to fifth.
City twice threw away the lead given by Yaya Toure and Edin Dzeko before Andreas Weimann struck Villa's winner.
Tottenham showed they should be held up as a title contender by holding Chelsea to a draw at White Hart Lane, although they will be disappointed they couldn't kick on after Gylfi Sigurdsson opened the scoring.
Chelsea seized the initiative in the second half and John Terry equalised with a header from Juan Mata's free kick, but hopes of victory receded with about 10 minutes to go when Torres was shown a second yellow card for a crash with Jan Vertonghen.
Cardiff inflicted more misery on Fulham after Jordon Mutch scored the winner in injury time. Steven Caulker's opener for Cardiff in the 12th had been cancelled out in the 45th by substitute Bryan Ruiz.
English Premier League
Tottenham 1 Chelsea 1
Aston Villa 3 Manchester City 2
Fulham 1 Cardiff City 2
Hull City 1 West Ham 0
Manchester United 1 West Brom 2
Southampton 2 Crystal Palace 0
Swansea 1 Arsenal 2
Overnight
Stoke v Norwich, Sunderland v Liverpool.
Tomorrow
Everton v Newcastle
- AP
