After Olivier Giroud gave the Gunners the lead, Villa - who spent much of last season battling against relegation - responded in emphaticstyle thanks to a brace from Christian Benteke and a debut goal for Antonio Luna.
Arsenal hadLaurent Koscielny sent off for two bookings and rallied with 10 men, but were not able to break down a determined Villa defence, as goalkeeper Brad Guzan made a couple of smart saves.
"I think everybody up and down the country would have thought it was a home banker really, but I have got lads in there who are really good, top footballers," said Lambert, whose side travel to Chelsea on Wednesday night.
"The no-fear attitude was key. Because we are young, everyone probably thought there would be an adverse reaction to it, but I have got to give them a lot of credit."