Villa were beaten 2-1 by npower Championship side Millwall in Friday'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 Friday's 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.
And Millwall boss Kenny Jackett told his side's official website: "I thought it was a terrific performance from the whole team tonight [Friday].
"I thought we deserved to win and I was so pleased for John Marquis that he got the winning goal. He has been out for a long time and has worked so hard to get back to fitness."