Lambert said he was "gutted, hurt, disappointed," after Villa's best hope of a season-saving Wembley final was snuffed out by opponents whose most expensive player cost 7,500 pounds and was stacking supermarket shelves to earn extra cash not so long ago.
"You can either lie down or come out fighting and I will come out fighting," said the Scot, whose side will play second tier Millwall with some trepidation in the FA Cup Fourth Round on Friday.
Tuesday's 4-3 aggregate defeat was a night of reckoning for Villa, whose main focus now will be on fighting their way out of a tough relegation battle with an inexperienced squad short of belief and leadership on the field.
Lambert joined the 1982 European champions from Norwich City in June, with Villa's American chairman Randy Lerner looking forward to a return to the sort of "compelling play" expected by fans.
"We will never have a better chance to get to a Cup final throughout our whole careers," Lambert told reporters on Tuesday as Bradford celebrated with some of the 6,500 visiting fans chanting "You're getting sacked in the morning".
"I can't repeat what was said to the players in the dressing room and no manager would tell you that, but everyone is hurting. They might take 10 or 12 years to even get close again," said Lambert.
"I know exactly how our fans are hurting because I am hurting exactly the same. The crowd were right with us and we let them down."
