Fr. Garrigou-Lagrange, O.P.'s The Principles of Catholic Apologetics: A Study of Modernism Based Chiefly on the Lectures of Père Garrigou-Lagrange, O.P.'s «De Revelatione per Ecclesiam Catholicam proposita» Adapted and Re-Arranged contains a very good criticism of the "New Apologetic" (p. 28, 42-43):
The method of Immanence…in human nature presupposes an exigency for the Supernatural … Before proceeding to note how the advocates of this new Apologetic regard criteria external and internal, the reader will distinguish [cf. Pascendi §19] between (i), the doctrine of "immanence," i.e. God's intimate presence in His creation of which the complementary truth is God's transcendence—acknowledged teaching of Catholic philosophy, and (ii), the doctrine of "immanence" in apologetics which accepts the internal religious sense as the only valid criterion of religious truth [cf. what I quoted above]—one of the fundamental tenets of Modernism. … Criticism of the New Apologetic 1.— It is founded on Semi-Agnosticism, vis, untrustworthiness of speculative reason. [Giussani: "The summit of the conquest of reason is the perception of an existing, unreachable unknown."] 2.— It is founded also on an aspect of the doctrine of immanence. If Catholic Faith is demanded by our nature, that Faith is not in truth the supernatural. In truth the Supernatural is above not only the powers but the exigencies of human nature. These Apologists fail to see that it is natural happiness arising from the natural knowledge and love of God that our nature strives to attain. [cf. Feingold's The Natural Desire to See God According to St. Thomas and His Interpreters and this The Thomist review of it] 3. — The formal motive of Faith consists in the authority of God who reveals, and not in religious experience.
Also, he considers Card. Newman one of the apologists who "appeal to internal criteria" (p. 41), as does Giussani; however, he doesn't appear to consider Newman a New Apologist like Blondel, as he likely would consider Giussani.