Your private prayers do not have to be theologically correct. They need to be honest and open to God to straighten out your theology.
Perhaps public prayer in a leadership function needs to be a bit more refined because we are leading the people in prayer. But this is a private heart prayer that the psalmist prays. It just gets public exposure.
In one of his better moments, King David had some insight into how to handle criticism:
Be not silent, O God of my praise!
For wicked and deceitful mouths are opened against me,
speaking against me with lying tongues.
They encircle me with words of hate,
and attack me without cause.
In return for my love they accuse me,
but I give myself to prayer."
- Psalm 109:1-4 ESV
Then, he goes downhill a bit and starts praying curses on his enemies.
But then, he comes back to his own feelings. He is being honest with God about how he feels.
He puts his enemies in God's hands Who is a whole lot more merciful than he knows and he ends on a positive note:
" With my mouth I will give great thanks to the LORD;
I will praise him in the midst of the throng."
-Psalm 109:30 ESV