Paul Lambert was "gutted, disappointed and hurt" after the Capital One Cup semi-final exit at the hands of Bradford City.
Lambert was upbeat after the first-half display which saw Christian Benteke give Villa a 1-0 lead.
But James Hanson's goal from a set-piece resulted in "edginess" from his team and they were unable to secure the two goals needed to take the tie into extra-time.
The boss was upset at his team not taking their chance and reaching Wembley - and also their concession of another set-piece, after three in the first-leg.
He said: "I am absolutely gutted, disappointed, hurt, everything.
"Everyone is hurt. You will never have a better chance to get to a cup final throughout your whole career, even the young lads.
"It may take them 10 or 12 years to get even close to one again. That's the hurt.
"In the first half, we looked really fine, we looked good, we got a goal and you thought we'd go on and get the chances.
"Once they scored, the edginess came in and we started to play long balls. We don't have the players to play long balls. That's where it becomes a bit edgy.
"Even then, Andi scores and you think something might happen. But first half we should have got one or two. But again we got done by a set-piece.
"That's two semi-finals where we have lost four goals from set-pieces. The set-pieces are a concern. We practice them every day in training.
"If you have a man in the penalty area, you have to be prepared to compete with him.
"Everyone knows their job and who to pick up. It's man for man. It's me against you. That's your job. You know who you're picking up.
"You know what you're doing for corners and free-kicks. That's not hard to understand. That's black and white. It comes from an individual. It's me against you."
Lambert said he felt the team had "let the fans down."
He continued: "I am every bit as hurt as what they are. It's my responsibility. I know exactly what it's like and I know exactly what they're feeling because I am feeling the exact same.
"We played really well in the first-half. The atmosphere was brilliant. The crowd are right with you and we have let them down. The bottom line is we have let them down."
Lambert said his side would now come out and fight with an FA Cup tie with Millwall on Friday, followed by a Premier League encounter with Newcastle United on Tuesday.
He added: "There are two ways - you either lie down and accept it or you come out and fight. I am certainly not going to lie down.
"I have never done it. I will come out fighting.
"You have to pick them up. They have a game in a few days time. Fans will come a long way to watch it. You have to pick yourself up."
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