Villa were beaten 2-1 by Championship side Millwall in Friday night's FA Cup fourth round clash at The Den, adding to Tuesday's Capital One Cup exit to League Two Bradford and their Barclays Premier League struggles.
But, asked whether he hopes to remain in his post, Lambert told Sky Sports News: "There's no point in asking that, of course I am.
"I'm not a quitter, I'll keep going."
The Scot added of the match: "I thought we dominated the game and I don't think we should have lost, at the very worst it should have been a replay.
"The first goal was a set-piece again and the second was just a crossed ball. The first was just a bog-standard corner, you've got to rely on individuals to go and compete.
"I thought it was going to peter out to a replay. We'll take the knock but you have to come back strongly."
Darren Bent had given Villa the lead but Danny Shittu equalised before John Marquis headed a late winner at the second attempt.