You do not have to analyze music using Roman numeral analysis.
Some music - Impressionism like Debussy - does not fit neatly into Roman numeral analysis.
Two common harmonic devices that often don't fit Roman numeral analysis are:
- chromatic mediants
- chord planing.
A chromatic mediant example would be like
D minor to
Bb minor. The Roman numeral analysis would be
bvi but the important thing is that isn't one of the usual chords in minor. You can read more about chromatic mediants at Wikipedia.
Chord planing is when you use one chord type and just move it in parallel fashion. In your example
C# major to
D is a kind of planing, but usually you would have the parallel motion move more than just one step. When the motion involves only two chords by a halfstep as in your example you might describe it as a kind of appoggiatura chord.
Back to your example:
D F#m A C#m C#
All but the last
C# major fit into the key signature for
A major where the first four chords would be
A: IV vi I iii.
But then some might think it clever to say it fits into
F# minor as
F#m: VI i III v V
The problem with both - or any other attempt to label "the key" - is the harmony doesn't do anything to actually confirm a key. Specifically there isn't a cadence.
I think the important thing about the progression is that it moves mostly by ascending thirds. In the tonal major/minor key system that is a weak progression. By "weak" it really means not a strong way to define a clear key. It doesn't mean bad harmony. This kind of harmony can have a very gentle flowing feel that would not be found in music like Haydn's, but would seem to work well with ambient.
You might think of this kind of harmony as anti-cadential because it seems to avoid cadential patterns. But if you consider that a cadence functions to stop the flow of the music, it makes sense to take an anti-cadential direction in ambient music where you want the music to sort of float endlessly.
It may help to think in terms of diatonic harmony versus being in a key. You can select chords from a key signature like
A major without formally being in the key of A. You might look into modern modal music or pan-diatonicism to get an idea of how that can work.
I sense you are already on the right track. You don't need to formally define a key. You do not need to approach harmony with only Roman numeral analysis. Try reading up on the modernists of the 20th century like Debussy, Ravel, Bartok, Stravinsky, Hindemith, Poulenc, Milhaud, etc. Stylistically some of that music is brutal and not at all like ambient, but it will give you a whole new set of analytically terminology to use when approaching your own music.