The Spirit of Christ was working in the writers of the Psalms, and was sharing in their distresses and joys and was at one with them (compare Is. 63:9; 1 Peter 1:11).
Christ is very distinguished in the “messianic psalms” but many psalms are referred to Him in the NT (and these are not the so-called messianic psalms).
The following Psalms ought to be mentioned especially:
Psalms 2:7 – “Thou art my Son: this day have I begotten thee” (Acts 13:33)
Psalms 8:6 – “Thou hast put all things under his feet” (Hebrews 2:6-10)
Psalms 41:9 – “Yea, mine own familiar friend, in whom I trusted, which did eat of my bread, hath lifted up his heel against me.” (John 13:18)
Psalms 45:6 – “Thy throne, O God, is for ever and ever.” (Hebrews 1:8)
Psalms 110:1 – “The Lord said unto my Lord, Sit thou at my right hand.”(Matthew 22:44)
Many more references could be added. Nearly half of all messianic references in the NT originate from the Psalms.
The Spirit of Christ unites with the experiences and feelings of these believing Israelites.
This is why the sufferings of the Lord and His feelings as true and perfect man are described in the book in such touching manner, for they are a proof of His interest in His earthly people.
Describing the history of the Jewish remnant in the last days reflects the prophetic character of the Psalms.
But again not the outward events are described but the inward feelings.
This would also explain the pleas for punishment or for vengeance on the enemies (e. g. Psalms 137:9), which are difficult to understand for many a reader.
The feelings explained in these Psalms are feelings of believers but not of Christians living in the household of grace (compare Romans 12:17-21).
They are feelings of believing Jews living in the coming last days.