American goalkeeper Brad Guzan saved four penalties - one at the end of normal time from Kenwyne Jones and three in the shoot-out which followed a goalless 120 minutes - as Villa edged into the last eight.
A disappointed Bruce said: "We had more chances than them but it wasn't our night.
"We have a lot of disappointed people. But I thought our overall performance was excellent and in my opinion we deserved to go through.
"Their keeper had one of those nights he will remember for the rest of his career."
"We had chances, the penalty, and Kieran (Richardson) had an opportunity in the final minute but we weren't able to take them."