Steve Bruce's men went down 3-1 on spot-kicks as Andy Reid, Lorik Cana and Jordan Henderson all saw their efforts saved by Villa hero Brad Guzan.
The American stopper had earlier saved a Kenwyne Jones towards the end of normal time, and the keeper
made a string of saves to keep the Black Cats at bay.
The Wearsiders must be rueing the ones that got away, in particular Kieran Richardson who should have scored towards the end of extra-time.
The midfielder latched on to a long clearance and raced in on goal, but his shot was straight at Guzan.
You got the feeling that miss would come back to haunt the red and whites, but Richardson was not alone.
With seven minutes of normal time remaining Kenwyne Jones could have decided the tie from the penalty spot.
Referee Phil Dowd awarded the spot-kick after handball by Carlos Cuellar and up stepped Jones only to see his shot saved by that man Guzan.
It was a preview of what was to come, as time and time again the Villa keeper guessed right during the agonising shoot-out.
To be fair, the Wearsiders were the better team throughout the match and tested Guzan on several occasions – Henderson's shoot on sight policy almost paying off.
The youngster forced two good saves out of Guzan and also went close with another couple of efforts.
It was close, but not close enough for the Wearsiders, as Villa rode their luck and lived on half chances.
The visitors seemed prepared to sit and wait and try and hit the hosts on the break, although Sunderland keeper Craig Gordon was rarely tested.
Martin O'Neill's men were much brighter in the second half, but again their breaks were far too sporadic and lacking any real venom.
That didn't matter at the end of the night as the penalty agony proved a real sting in the tale for Sunderland.