Played on a line with Mikael Andersson and Arto Sirviö in his rookie year. In 1990-91, he played with Peter Berndtsson and Niklas Andersson, forming the famous "ABC Line". After Niklas Andersson's departure in 1991, Terho Koskela joined the unit. Carnbäck almost left Frölunda in 2000, due to Frölunda's questionable fiscal situation and a disagreement with head coach Tommy Boustedt. However, Carnbäck agreed to a three-year contract extension in the end. Then in 2003, the 35-year-old finally won a Swedish Championship and retired the same summer.
Carnbäck now runs a hockey talent agency (AC-Hockey) with former teammate Patrik Aronsson. (2011)