"We just didn't turn up in the first half," Levein said.
"We had a game plan. Bougherra wasn't playing so we told them to get the ball into the box.
"We have good headers and good crossers of the ball.
"For some reason, in the first half, we decided we weren't going to put the ball in the box.
"We had our defence to thank for keeping us in it."
Levein, whose side have now lost just once in 15 games, added:
"I'm thrilled to bits. At half-time, I was looking at a 2-0, 3-0 or 4-0.
"If you had asked me then, I would have been delighted with a draw.
"We were a different team altogether in the second half."