Verses 1-18 praised God and glorified HIm, especially for HIs lovingkindness and faithfulness

Verses 19-37 celebrated God's lovingkindness and faithfulness in the promises to David

Verses 38-51 But not introduces this section where it does not seem the promises of God have been fulfilled

It seems like what was promised the kings from the line of David has not been fulfilled.
89:42 is a good illustration of this.
Exalted- God is exalted in 89:13 and the people are exalted by God in 89:16, 17 and the king is exalted in 89:19, 24. But now the adversaries are exalted.
Right hand- God's right hand was exalted in 89:13 but right hand of the king is exalted in vs. 25. The right hand of the adversaries are exalted.  
Adversaries- The adversaries were to be crushed in vs. 23 but now they are exalted.

Jesus answers Psalm 89:38-52
He is God's anointed (38, 51), God's servant (39), and He was made an object of reproach (50-51).
89:49 The cross and resurrection are the ultimate answer to the questions "Where are Your former lovingkindnesses, O LORD, which You swore to David in Your faithfulness?"
89:48 Jesus provides an answer to the problem of death.