The old way of quoting likely demanded a greater view of context. Take for example:
Then was fulfilled what had been spoken by the prophet Jeremiah, saying, “And they took the thirty pieces of silver, the price of him on whom a price had been set by some of the sons of Israel,” (Matthew 27:9 ESV)
The above reference to Jeremiah has caused no little consternation among interpreters, because the quote is more clearly from Zechariah. Some state that there is a clear reference to Zechariah 11:12–13 and Jeremiah 19:1–13, but I would add that I immediately think of Jeremiah 32 where Jeremiah did in fact buy a field. Some go as far as saying the reference to Jeremiah is a complete mistake (Calvin), a copyist error; to which of course would not effect a bit of our faith in the Bible if it was properly proven such. Nonetheless, the explanation here is likely far less demanding than bearing that aforementioned burden of proof.
In earlier times there were no chapters and verse numbers per se, therefore referencing books involved stating what was often the first or predominate book referring to the whole. In the case of referring to a Psalm in particular, the Hebrew would quote the first verse (think of Jesus on the Cross quoting from Psalm 22). In the case of quoting whole sections in reference, Jesus spoke of fulfilling the law, prophets, and psalms; speaking of the whole of the Old Testament. In the case of Matthew 27:9 what is likely going on is that it is a quote from Zechariah, a minor prophet, whose writing was contained near or in the same scroll as Jeremiah; and thus to the original reader it was simply a reference to such.
Therefore, we learn that referencing of texts in days prior is quite a different world than today. I am not sure we have improved in offering chapter and verse, because there is something to those who know their Bible so extensively as to speak of whole scrolls rather than the common method of extracting verses from this book or that to prove a point. It seems from the Hebrew mindset at the time likely that a much larger context was always considered in the quotation of Scripture. They could identify when a mere phrase was quoted in a much larger work. We are prone to ask for numbers (chapter and verse); they were more prone to think of actual people whose names were on scrolls and took them to the address of the quote in mind. Their Bible study was indeed much more (literally) personal and contextual in that way. This was simply an older (and in no way inferior) way of quoting Scripture.