"We always work hard and that's something our supporters have always come to expect.
United are now unbeaten in eight matches as they prepare to face Rangers in the CIS Cup Final on Sunday.
"Tonight was a point a lot of teams round about us wouldn't have expected us to get. It keeps our run going.
"I don't think our goalkeeper has made a save of any great significance. We've had the best chance of the match, with Conway's header from six yards," added Levein.