Well, in this case it sounds like you caught the plagiarism without needing to use the software. How? Because the student plagiarized from one of the course readings, and as it happens you are very familiar with the course readings.
It seems to me that this "human plagiarism catching" can be generalized: you don't have to be able to have software to trawl the internet for copying if you yourself know -- or even have a sufficiently good idea -- which material is likely to be plagiarized. In my experience the average student is remarkably bad at getting academic information from the internet: they don't know enough to rapidly and accurately sift through the deluge, so they hold tight to whatever was high on the first google search screen and succeed or fail accordingly. If you are concerned about plagiarism, I think it would be time well spent to search the internet before making the assignment and bookmark the most plausible sources to be plagiarized. This won't catch everyone, but then again nothing will. If you feel strongly enough, you might even design some initial assignments as "plagiarism bait". As long as your goal is to teach your students right and wrong rather than a priori to get them in trouble, I think this is an entirely justifiable thing to do. Also showing someone that they have already gotten caught and gotten in some trouble can be a great motivator for keeping their nose clean in the future (or, sure, digging much deeper in their dishonesty, but again one has to play the percentages here).
Good luck. I don't work in a field in which plagiarism in papers is common -- I am a mathematician -- and the idea that university students regularly commit such dishonorable acts disgusts me. Anyone who wants to take a harder line (and of course who informs and educates the students in advance) has my full support.