A weakened Villa side conceded three goals in four first-half minutes to set the Gunners on their way to a win, and despite a good second-half performance by captain Gabriel Agbonlahor, they were never able to get back into the game.
Lambert told reporters after the game: "You try to play everything down but Ashley Westwood was being sick in the warm up and Andreas Weimann was getting it during the game. Nathan Baker and Darren Bent were also out with it.
"To play Arsenal you need everyone fit. The players have been brilliant so far this season and if somebody had said we would have 10 points by this time I would have taken it.
"We are probably going to let the lads stay away for a couple of days. The staff have got it as well. I don't know what kind of virus it is but it is certainly doing its job."
Despite the result, Villa remain third in the Premier League table.