Brillat played for the youth teams of sports community SG Berolina Straulau in East Berlin.

Among his teammates in the youth team were future DDR-Oberliga players Frank Terletzki, Wolfgang Filohn, Rainer Rohde and Gerald Schwierske.

Brillat made his first appearance with the first team of BFC Dynamo as a 19-year old in the 22nd matchday of the 1969–70 DDR-Oberliga at home against Hansa Rostock on 2 May 1970.

He would line up against players such as Michel Platini, Trevor Francis, Kevin Keegan and Peter Shilton.

[5][2] Brillat says that a moment he will never forget is running onto the pitch at Anfield in the third round of the 1972–73 UEFA Cup match against Liverpool F.C.

[5] He has made regular appearances with the traditional team of BFC Dynamo since retiring from professional football.

[6] Brillat participated in Christmas festivities with the traditional team as of 2022, together with other former teammates from his professional career, such as Wolf-Rüdiger Netz, Bodo Rudwaleit and Christian Backs.