We have been given authority over all powers of the enemy (Luke 10:19 & Mark 16:15-18). I believe with authority, we are given responsibility.
I don't believe we are to pray and ask the Lord to cast the demon out, I believe that is something we ourselves are to do. I know when it comes to binding and loosing, there is nowhere in the NT that it tells us to pray and ask God to bind the devil. But it does say that WE are to bind, and WE are to loose. Matthew 16:19, "And I will give unto thee the keys of the kingdom of heaven: and whatsoever *thou* shalt bind on earth shall be bound in heaven: and whatsoever *thou* shalt loose on earth shall be loosed in heaven." Jesus gave us the keys, but it's up to us to use them!