And the Gunners' England star Theo Walcott put the boot into the Premier League strugglers, claiming Villa were totally overwhelmed in the second-half.
The relegation-threatened side conceded four second-half goals in the last 34 minutes, leaving their Scottish manager disgusted.
"You probably can't print the things I'm feeling," said Lambert, whose side have now gone over 10 hours without a Premier League goal.
"I don't like being in this position, we've been in this position for too long.
"Since I've been here it's always been fight, fight, but you've got to keep going, you don't throw the towel in.
"I thought for 60 minutes of that game we were well in it. The disappointing thing for me was the acceptance to lose more goals."
Walcott also felt Villa had been swept aside after the break.
"In the second half, I can't think of a more one-sided game," he said.
Goals from Olivier Giroud, Theo Walcott, Mesut Ozil, Walcott, a Santi Cazorla penalty and Hector Bellerin, ensured Villa stayed just three points off the drop zone.
Their third straight win in the league saw Arsenal leapfrog London rivals Tottenham to go fifth.
Arsene Wenger was thrilled to see England star Walcott - who was kept out for a year through a serious knee injury - score his first League goal for 14 months.
But the Arsenal boss insisted the 25-year-old, who was making his seventh appearance since his comeback, was still had some way short of his best.
"In his overall game, he still needs some more sharpness or contact," Wenger said.
"In the first half he was through when Jores Okore caught him back. Once through nobody usually catches him back.
"He must get used to physical contact, but in every game he's stronger."
Wenger also felt German star Ozil, who is also coming back from a knee injury, can only get better.
"I think he still lacks a bit of competitive edge on sharpness front, but the quality of game is exceptional," Wenger added.
"He's getting back. He's worked very hard physically and he's ready to play again."
