Craig Levein lost his job as national team manager after Scotland picked up just two points from their opening four matches and Miller has admitted that he and his teammates feel as though they have let down the former Leicester City manager.
Miller said: "There are a few of us who felt we let the manager down in the performances in the first four games. It's not the return we hoped for and thought we would get.
"Going into this campaign I was as optimistic as ever. I felt we had a good group and the group was very open, but when we have crossed that white line we have just not performed as players.
"It's very disappointing because we are playing catch-up in the group and ultimately it has cost the gaffer his job."
The 32-year-old forward has scored 17 goals in 64 appearances for his country.