St Pat's went out fighting but failure to take chances put an end to their European run.
Tempers boiled over on the final whistle in Tallaght after CSKA overturned a 1-0 aggregate deficit to progress 2-0 on the night and 2-1 overall.
Saints midfielder Jamie Lennon and CSKA’s Bradley De Nooijer squared up to each other after the final whistle and it sparked a melee involving most players.