The NPP diminishes the atonement of Jesus Christ in several ways:
1) Sanders and Dunn argue that Paul's main ideological emphasis inherently focused on the Jewish participant in a form of mystical-spirituality with Jesus Christ. Thus, Paul's language (i.e. Scripture) was not judicial language (i.e. justification), but was a subordinate-type to the participate language, basically declaring mystical-spiritual religious life was a way of maintain salvation/sanctification in the first century. This is a covenantal-nomism understanding of the atonement, and deems it unsatisfactory or unnecessary since a relationship with God does not demand a payment of sin but a spiritual reconciliation.
2) N. T. Wright argues that Paul views Israel as only a representative of humanity and taking onto itself the sinfulness of humanity through history culminating in Jesus Christ. This is a kind of historicized-reconstructionism of Paul's Jesus and his understanding of the atonement, and deems it symbolically remedial.
The NPP basically means you can know God without his righteousness that is provided through the atonement of Jesus Christ.
I find it unfortunate and agree with Piper when he explains how the atonement is diminished by the new perspective on Paul, "The faith that justifies continues to hold fast to Christ alone as the ground of our having God as our Father who is completely for us. Whether this right standing with God consists in the imputation of righteousness from beginning to end or consists partly in the impartation of righteousness is a crucial and necessary question [because if answers wrongly, like N.T. Wight, it diminishes the atonement!]."
There is a reason why Paul says, "For we are the circumcision, who worship by the Spirit of God and glory in Christ Jesus and put no confidence in the flesh" (Philippians 3:3 ESV).