The Psalms may have been used as a type of the writings, as the dominant writing. I dont' know that we have enough information to be dogmatic that Jesus was using "Psalms" as a generic, but as a practicing Jew he would have been reading from the Tanakh which was an acronym for Torah Neviim and Ketuvim (or the Torah, the Prophets, and the Writings). Its composition was laid out by the Anshei K'nesset HaGedolah or the Men of the Great Assembly. Its also said that many of the prophets whose names grace the books of the Old Testament were a part of them and probably had a role in determining the Canon for the Jews- however, as you know God has verified what He considers Scripture over and over again by the cross-references you find within Scripture itself.
There is another great chart at http://www.bible.ca/b-canon-old-testament-quoted-by-jesus-and-apostles.htm
Here, they say that
1)The New Testament quotes from all Old Testament Books except Ezra, Nehemiah, Esther, Ecclesiastes, and the Song of Solomon.
2)And Jesus quoted from 24 different Old Testament books.