A goal by Rodrigo Tello after 20 minutes gave Besiktas their first win at the fifth attempt in Group B.
Foster was left stranded as Tello's effort rebounded off left-back Rafael and deceived him.
It was a cruel blow for Foster on his return between the posts for United for the first time in a month.
Ferguson said: "The goal followed a deflection off Rafael and we were chasing the game. Deflections off the body have a certain speed and that can cause a problem."