The former Blackburn manager felt the Blues should have built on the lead given to them by Gelson Fernandes just after the hour mark rather than be forced to extra-time and then ultimately spot-kicks.
Hughes said: "We are disappointed because we had a strong enough team out there to have won this game and I thought we looked very comfortable in the second half.
"But we missed chances when we should have been professional enough to have seen it through to the end after taking the lead.
"Once it goes to penalties it can go either away so we mustn't dwell on this result but you never want to go out of any competition."
He added: "There is obviously a lot of focus on us at the moment but I don't know if I'm more embarrassed than angry about going out.
"At least we were able to give game-time to some players who needed it - and to be honest the need was pretty evident at times."
Hughes rested Robinho and Shaun Wright-Phillips with one eye on Sunday's trip to Wigan.