The piano player is working around the bass notes and the quartet notes. In the key of D minor(F major6) you have of pallet of chords that fit this song.
D minor
C major
E minor
F minor6
G major7
A major7
All your chords follow this scale D, E, F, G, A, B, C, D. If you haven't learned how to chord scales this I will give you the pattern I also teach on my site.
D= F A D
E= G B E
F= A D F
G= C E G
A= D F A
B= D G B
C= E G C
D= F A D
Now these chords are used adding all the elements of chord e.g. 6th, 7th, dimished etc. You bounce off these chords using F# B, E Bb, F B.