The Scots headed into their clash with Belgium knowing they needed a victory in Brussels to have any real hope of salvaging an ailing campaign.
A win would also have eased the pressure which has been mounting on the manager, following home draws against Serbia and Macedonia last month and Friday's loss in Wales.
Instead, goals from Christian Benteke and Vincent Kompany handed the Belgians a 2-0 win to leave Scotland's hopes of reaching Brazil in 2014 in tatters.
Asked if he would consider his position, Levein said afterwards: "Not at all. I'm very proud to be the Scotland national team manager and I want to continue to do so.
"I've been in football for long enough to understand when the players are trying at their maximum and they're doing their best for each other and for the team - and they did that tonight and on Friday night.
"They didn't have any energy left at the end of the match and they did everything possible to get a result for Scotland tonight.
"I've seen again tonight a group of players who are determined and hungry and desperate to do well for Scotland.
"As long as that is the case, I'm quite happy to be working with these players."
Of course, the decision could be taken out of Levein's hands by his bosses at the Scottish Football Association.
He added: "All I can tell you is that I want to remain as the manager - that's what I want to do.
"Other than that, you will have to ask other people the questions you are asking me.
"As far as I am aware, I'm still doing my job so you would have to ask other people the questions. It's impossible for me to answer.
"I'm interested in staying in the job and working hard to improve things."