You got a source for a New Testament scripture that says "toss out the Psalms?"
Got one that says include them? Psalms are songs of praise to God. Any method of worship mentioned in the Psalms would have to have been acceptable within the old Law. Christians are not under the law, therefore methods of worship that were once acceptable may no longer be. Sacrificed any animals lately?
Christians must look to the NT for acceptable worship.
Galatians 3:24 Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.
25 But after that faith is come, we are no longer under a schoolmaster.