Wow thats quite a long walk from terminal f to terminal d and back to catch your flight in terminal F
must have had a long transit time or you was at the airport really early.
I remember they had a list of cards thats eligible for entry unless you used the printed lounge card that comes with your boarding pass.
I remember 3-4 years ago when i flew SVO-HKG terminal F( terminal 2 they used to call it )there was 3 different lounges one for Aeroflot members (second floor)the other for korean air(outsourced) (Ground Floor) and another for air france klm (outsourced) (second floor)
I tried the korean air one as it was better and they said no go to the aeroflot lounge one floor up.
To be fair it was a privately owned LLC that operated the lounge on behalf of Korean air and I think the airline pays them per guest.
That could be the reason here why you were denied access
I flew HKG-SVO they made me use the Cathay Pacific Lounge when SU had a code share with CX.
AFKLM woulnt let me into theirs in HKG until I Showed them FB card.
Now Aeroflot uses travellers Lounge (outsourced) and i coulnt gain entry with FB or aeroflot as my flight was with china airlines.
I did get into the korean air lounge and china airlines lounge though with fb and aeroflot gold I guess because its actually airline owned and operated.
Hope this Helps I dont think the Lounge is Owned by Aeroflot in Terminal D