Villa had already qualified from Group F, but passed up the opportunity to progress to the last 32 as top seeds in their section after playing second fiddle to a dominant Hamburg unit.
Martin O'Neill opted to rest a host of key players ahead of the busy festive period and the gulf in class between Villa's fringe players and a home side currently riding high in the Bundesliga was apparent from the start.
Gabriel Agbonlahor, Ashley Young, Martin Laursen, Gareth Barry and James Milner were all left at home as O'Neill included only three of the side which started last weekend's Premier League victory over Bolton Wanderers.
Villa struggled from the off and after a slow start the visitors found themselves a goal down on 18 minutes.
In-form Croatia striker Mladen Petric took his tally to six goals in his last seven games as he brought down a long diagonal pass from the back with a lovely touch before burying a low left-foot volley from the edge of the box into the bottom corner.
Back-up goalkeeper Brad Guzan was picking the ball out of his net again on the half-hour mark as Ivica Olic dived bravely at the feet of Carlos Cuellar to meet a cross with a downward header which found the net from six yards out.
Piotr Trochowski should have made it 3-0 on 33 minutes but side-footed a volley straight at the keeper, while Marcell Jansen rattled the crossbar with a superb shot from 30 yards on the stroke of half-time.
But the third goal duly arrived 15 minutes into the second half, albeit in somewhat bizarre circumstances.
Craig Gardner was lying prostrate in the Hamburg box following a collision with the keeper but, when the defence cleared their lines, Olic was first to react and he held off two weak challenges before lashing a left-foot shot past Guzan.
Gardner could not continue following his clash with Frank Rost and limped off to be replaced by youngster Barry Bannan.
But Villa were denied any further embarrassment as former Spurs and now Hamburg coach Martin Jol took off Olic and then Petric in an attempt to protect his impressive strike duo.
Nathan Delfouneso did reduce the arrears with a fortuitous goal in the 82nd minute when Moustapha Salifou's wayward shot deflected off his leg and past the flat-footed keeper.
But any slim hopes of a Villa fightback were ended with the dismissal of Steve Sidwell for pulling back David Jarolim to needlessly earn a second yellow card almost immediately from the restart.
Hamburg successfully played out time to secure their passage to the knockout stages as group winners, while a late collapse has left Villa in third and facing the prospect of a tricky last 32 tie when Friday's draw is made.