The Midlands club are currently one place above the Premier League relegation zone and were also knocked out in the semi-final of the League Cup by another fourth tier side Bradford City on Tuesday.
"It's not great, but you have to keep going," Lambert told the BBC.
"You take your medicine, pick yourself up and go again. There's no way you can lie down."
Villa fans have pinned a lot of the blame for the club's current predicament on owner Randy Lerner for failing to invest sufficiently in the playing squad, but Lambert defended the American.
"Randy has been brilliant," said the former Norwich boss. "Whatever happens happens, but he's been brilliant with me. He's a really good guy."
Villa took the lead on Friday through former England striker Darren Bent, but the Premier League strugglers were then rocked by goals from defender Danny Shittu and forward John Marquis.
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