A late double from Gareth Bale handed Chris Coleman's men victory at the expense of the visitors, who have collected a meagre two points from their first three World Cup 2014 qualifiers.
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"Leaving? No chance," he declared. "It's a job I really want to do. I love doing it and it's important we pick ourselves up and go again."
The 47-year-old, who is approaching his third anniversary in the role, conceded that his side must now pick up all three points at the expense of in-form Belgium when the two teams clash on Tuesday.
"It leaves us needing to win the game on Tuesday, that's for sure," Levein noted. "It is a difficult task, but it's a different game altogether on Tuesday.
"A victory tonight would have made it a little bit easier - even a point would have been worthwhile on Tuesday - but I think now we've got to go and try to win the game."