In the Preface to the Critque of Pure Reason Kant says "I had to deny knowledge in order to make room for faith."

The Critique of Pure Reason places limits upon Reason. It introduces the idea of the noumenal world beyond sense and indeed beyond reason.

Romanticism followed in the wake of the Enlightenment. The Enlightenment thinkers were perhaps too optimistic as to what Reason could accomplish and sometimes what reason dictated was undesirable or depressing or just plain boring...there must be something more than this.

Kant famously kept a portrait of Rousseau on his wall. Rousseau came before Kant but his work was much less systemic and rigorous than Kants. With Kant Reason was turned back on itself to crtique itself. In the past Reason had critiqued Faith, Superstition, Matter, Spirit but with Kant Reason took a good look in the mirror and found something it didn't expect to find. Arguably Hume held up the mirror and described what he saw...but Kant found a plausible explanation for what was seen; Hume described but provided no explanation.

If Kant made room for Faith but it need not be of the dogmatic fundamentalist sort. New ideas and metaphysical systems arose after Kant that had some of the same characteristics of the old Faith and occupied basically the same psychic space but were at the same time anti-dogmatic and resistant to arguments based on authority and friendly to Reason though not necessarily beholden to it. So as it happened in making room for Faith, Kant also inadvertantly made room for Romanticism. Still I think Rousseau deserves more credit for the movement.

If by "faith" you mean "belief unsupported by evidence", then faith is virtually always dogmatic. Once one is willing to believe without evidence, what is it that is going to change the belief?

The reality is, faith is prejudice; it is judging before one gets the relevant facts. It just sounds better to call it "faith" than "prejudice".

Also, whatever is beyond the reach of reason simply cannot be known. About such things it is fundamentally a lie to have faith and pretend to know what cannot be known. Honest people do not pretend to know what they do not know.

You are, however, fundamentally right about how Kant helped bring on the irrationality of the Romantic movement. He gave it a more respectable veneer than Rousseau did, and consequently is, in my opinion, more important for it flourishing. But Rousseau was more romantic himself, so there is something to what you are saying about that as well.

I came across some things in my reading today that lead me to believe that the Romantics really took off with the Critique of Judgment which added some tools to the theoretical toolbox of aesthetics and established the aesthetic sense as independent of reason and raw perception. I don't recall where or if this aesthetic sense is mentioned in the 1st Critique; it is not the "transcendental aesthetic"; that is something else entirely. It is however, discussed in the 2nd Critique which I have read and the 3rd Critique which I haven't read but only read about. In the 2nd Critique I recall Kant treating the recognition of Beauty as a subjective experience as opposed to the recognition of Reason and Truth which steps over into the realm of the objective.

Schiller's Letters on the Aesethic Education of Man were greatly inspired by Kant's work. Schiller promoted the aesthetic sense as a sort of bridge between raw sensuality and a ethical understanding informed by Reason...a bridge between the subjective and the objective. I am very fond of this idea and I think it is one of the greatest contributions left to us by the Romantics. That Reason need not be submitted to because it's arguments are irrefutable and necessary but that rather we should learn to love it as the highest Beauty.

If one were to write a paper regarding Kant's influence on Romanticism it is the Critique of Judgment that profoundly influenced the romantics and really it is there that we must look rather than for example, the earlier and much more simplistic work Observations on the Feeling of the Beautiful and the Sublime although these observations do include some theories regarding the racial or national characters of various peoples: English, German, French and the idea of a national character of these various Peoples did become very important to many of the Romantics. But this obsession with nationality is more the product of the post-Reformation socio-political environment of the maturing Nation-State system than of any of Kant's innovations. The Germans would have been less concerned with such things if there had been already a unified Germany as there was already a relatively unified England and France.

I'm not very confident as to how this relates back to the comment in the preface to the 1st Critique about "denying knowledge in order to make room for faith" but personally, I tend to associate religious feelings with aesthetic feelings and vica versa. Making room for faith could be making room for the aesthetic sense... Incidentally, Bacon similarly conceded territory to Faith, revelation, morality, aesthetics, emotion and poetics when he deemed these to be outside of the domain of his project of Science.