Villa reached the 2010 final of the competition, losing 2-1 in controversial fashion to Manchester United, but since then their fortunes have nosedived.
Manager Martin O'Neill quit five days before the start of the following season after guiding Villa to three successive top-six finishes in the Barclays Premier League. Villa then flirted with relegation under Gerard Houllier and former Birmingham boss Alex McLeish, who failed to win over the fans and was ordered to slash the wage bill.
Lambert has since put the accent on youth - the average age of the squad is less than 24 - after spending £22million in the summer and Villa are facing a battle to preserve their top-flight status. But there have been signs of improvement and a four-game unbeaten league run was followed up with Tuesday's 4-1 win at Norwich to secure a place in the Capital One Cup semi-finals.
Lambert said: "I think we are an easy target for people saying we are a young side and all that, but the reality is we've been playing very well despite a tough run of fixtures.
"We've come through a really hard run with the two Manchester clubs and Arsenal in successive matches. That's really, really demanding with a young team.
"They need a bit of help but if you can give them time, and keep that collective spirit with the crowd we've got, they'll drive us on. We have done well going back to the last round of the cup at Swindon and then the win at Sunderland. I think in the last eight or nine games the only two defeats have been against the Manchester clubs.
"The cup win is a huge win for us and to have a semi-final, with full houses home and away, will be brilliant for the club."
Former Canaries boss Lambert added: "The club has had a lot of heartache for the past two years or so and fans haven't had a lot to shout about. But the semi-final really gives supporters something to look forward to in the New Year and is brilliant for the club.
"We have had the youngest team in Aston Villa's history, which is an incredible achievement and hopefully shows in the future, given time, that we can build on it and have a good side. We are slowly but surely getting there. We're doing really fine. It's another building block."
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