Although many people interpret what Jesus is saying in the first way, I believe, that He means for us to see it in the second interpretation. Jesus said that God's authority rests upon us. How little we know of who we are in Christ. What must be understood is that His authority is upon us whether we apprehend it or not. When we do not apprehend what Jesus is saying we are left powerless.
Power is the ability or capacity to act or perform effectively.
We have the authority but many of us have no power because we do not comprehend the authority. The lack of power is not because of the devil, or other people, but simply due to wrong conceptions, strongholds of thinking that keep us from understanding what Christ has done for us. Remember that Paul said the gospel is not about words but power. Jesus' statement is an assurance that you, as a believer, have the authority to act effectively. If we are unaware of our authority, we have no power, and are reduced to only words.