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.
The Birmingham-based side are 17th in the 20-strong table league, one point above the drop zone with resurgent Reading and perennial Premier League escapologists Wigan Athletic just below them on 19 points.
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.
That day is still a long way off.
Birmingham-based Villa splashed seven million pounds on Belgium international forward Christian Benteke in a 20 million-pound spending spree but have otherwise put their faith in young players with embarrassing and traumatic results.
An 8-0 mauling by Chelsea at Stamford Bridge last month, their worst ever in the league, and a 5-0 drubbing by champions Manchester City were low points in a mixed season but the Bradford defeat may prove a defining moment.
The League Two club are 61 places below Villa and are the first from the fourth tier to reach a major English domestic cup final in 51 years.
Villa, whose fans had hoped Lambert would bring back the good times after replacing the unloved Alex McLeish, beat Liverpool 3-1 at Anfield in December in a five-game unbeaten run that proved a false dawn.
They have won only four of their 23 league games, one less than Wigan. Only bottom side Queens Park Rangers have fewer victories.
"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."
