Lambert vowed to fight on as Aston Villa manager after a second dismal cup upset this week.
He 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: "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."