Aside from specific criticisms that Hegel made of Newton his overriding reason was ideological, and he hated not so much Newton as "Newtonianism" which he saw as a motivation for "degrading" of philosophy. Collection of essays Hegel and Newtonianism explores the issue at length, see especially Gower's entry.
"Newtonian" philosophers, like Locke and Hume, abandoned search for "truth in thought itself", and viewed themselves as "underlaborers" (Locke's infamous "philosophy is a handmaiden of the sciences"), which of course was anathema to Hegel's anbitious view of philolosophy as "thought as such", Minerva's Owl ("the product of thinking, thought as such, is the subject matter of philosophy"), domain of the Spirit. Empirical origins, "concerned solely with things in nature" may stimulate our philosophical reflections, must be "excluded from the treatment" of "real philosophy" even despite attempts to "derive general principles from our experience of nature". It is Newton's method that is woefully inappropriate for philosophy of nature, according to Hegel, specifics are just illustrations of it. Truth about nature is not to be discovered by gathering useful facts about the world, it is to be discerned by intellect alone. As Hegel declares in Encyclopedia:
"There is a fundamental delusion in all of scientific empiricism. It employs metaphyisical categories of matter, force,... generality, infinity, etc.; following the clue given by these categories it proceeds to draw conclusions... And all the while it is unaware that it contains metaphysics - in wielding which it makes use of those categories and their combinations in a style utterly thoughtless and uncritical (§38)... Newton gave physics an express warning to beware of metaphysics, it is true; but to his own honor, be it said, he did not obey his own warning (§98)... Physical mechanics is steeped in an unspeakable metaphysics, which, contrary to experience and the Notion, has the said mathematical determinations alone as its source (§270).".
In his rejection of "lowly" empiricism, and at its root Newtonianism, Hegel followed in the footsteps of romantic movement as a whole. Another prominent hostility came from Goethe's challenge to Newton's theory of colors. Goethe, the author of Faust, was Hegel's long term philosophical ally and correspondent. He emphasized "experience" of color rather than its empirical manifestations, Schelling had similar feelings on a grander scale. Romantics found the empirical science of the day wanting and distasteful, and dreamed of another, better "Science", speculative for Hegel, intellectually intuitive for Schelling, but devoid of Newtonian "bean counting" for both.
This hostility survived Newtonianism vs romanticism, one can see it replayed in Carnap vs Heidegger, the two cultures of science and humanities, the debates over the "true subject" of philosophy, and the analytic/continental divide. For these 20th century controversies see D’Agostini's From a Continental Point of View: The Role of Logic in the Analytic-Continental Divide:
"In fact, the wide interest in the nature of pure thought and pure theory (logic 2) for European philosophers (also neo-Kantians and neo-Hegelians) was partially connected to the effort made by philosophy to save its own primacy and identity while conserving its own ‘science of logos’ (logic 1) an aim successfully accomplished for the moment... psychologism was finally foiled in the 1920s. However, it was not on behalf of pure thought that the battle was won.On he contrary, the very adjective ‘pure’ soon began to fade, and there search culminated (for Heidegger since the 1923 winter courses on Faktizität) with the victory of impure existential thought."