Is the sermon on the mount intended for unbelievers?

I'd like to know if Jesus' sermon on the mount (Matthew 5-7) is directed at an unbelieving audience or an audience of believers. I'd argue its for unbelievers. At this point in time the disciples weren't truly believers (they wanted Jesus for political reasons, this was made clear when they left him during his final hour). The climax of the sermon Matt 5:48 "Be perfect as I am perfect" denotes condemnation since its impossible for anyone to achieve perfection without Christ. I'm under the impression it's geared towards unbelievers, to show them they are incapable of receiving salvation outside of Christ. Any problems with my thinking?