Villa visited Upton Park hoping to address their goalscoring problems in a city in which they had scored four goals in two games – against Arsenal and Chelsea – already this season.
Instead, Lambert's men drew 0-0 to become the first team in the 2013-14 Premier League campaign to go four successive matches without scoring a goal.
Since Andreas Weimann's winner in the 3-2 defeat of Manchester City in late September, Villa have now gone 375 minutes without hitting the net.
Striker Christian Benteke missed two headers he should really have scored, one striking the crossbar, while Weimann spurned a one-on-one opportunity with West Ham goalkeeper Jussi Jaaskelainen before hobbling off with a suspected hamstring injury shortly into the second half.
Lambert nevertheless said he is unconcerned by Villa's continued profligacy in front of goal.
Asked if Villa had the contest's best opportunities, the Villa boss responded: "I thought so, on clear-cut chances. Andy's (Weimann’s) first half - the goalkeeper's made a good save - and then Christian's header and Christian's shot. I think we had the three best chances of the game. On another day they go in.
"I can't be too hard (on the players). We're creating chances. I'd be sitting worried if we weren’t creating them, but Benteke's always been a threat. So has Weimann and to be fair, Jaaskelainen's made a terrific save from that one.
"On clear-cut chances (we came out on top). We've come to a difficult place. I’ve got no worry about us taking chances. No worries, none whatsoever."
West Ham's 4-6-0 formation is a new puzzle for teams to solve, but Lambert insisted that he focused on his own side's style leading up to kick-off.
"We've our own philosophy," he added. "We set up with a back three. We went to win the game. We played two up top. You can't get over-worried about somebody else's way of playing.
"You respect Sam's (Allardyce's) way of playing but we had to go and try and win."
The draw left Villa 13th in the Premier Legue, three points above the relegation zone. They return to action next Saturday at home to Cardiff City.
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