There are a large number of passages in the Old Testament Psalms – songs and poems that would have been as familiar to the Jewish people of Jesus’ day as our Catholic prayers are to us – that refer to Messiah (Christ):
Psalm 2 (See Acts 13:32-33)
Psalm 16
Psalm 22-The Crucified Messiah
Psalm 23-The Resurrected Messiah
Psalm 24
Psalm 34
Psalm 68
Psalm 69
Psalm 72
Psalm 91
Psalm 110
The book of Proverbs and the Song of Songs (Song of Solomon) are also replete with Messianic (Christ-ian) images that foreshadow Jesus’ life and ministry.
Indeed, the Old Testament from Genesis through Malachi is full of evidence that points to Christ. So whether one uses “Psalms” at face value or combines the word into meaning “Other Writings,” makes little difference! Jesus’ reference can just as easily refer to all the OT with its major sections of the Hebrew Scriptures known as Tanakh: Law (Torah), Prophets (Nev’im), and Writings/Psalms (Ketuvim).