Villa beat Norwich City 4-1 on Tuesday night to book their place in the Capital One Cup semi-finals and Lambert was delighted with the result, especially after recent fixtures against top teams.
"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," he said.
"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."
Villa will be joined in the league cup final four by Bradford City, who shocked Arsenal last night, whilst Swansea City take on Middlesbrough tonight and Leeds United host Chelsea next week to determine who the other two clubs will be.