The draw for the group stage of the Europa League takes place at midday BST, 7 a.m. ET on Friday, Aug. 26.
Ludogorets began with a two-goal lead, but Plzen made a game out of it early, before giving up two goals, losing 4-2 on aggregate.
The quarterfinalists from two seasons ago make it to the group stage with ease by beating Villarreal 3-1 on aggregate.
Roma crashed out of the Champions League before the group stage following two more red cards in a 3-0 home defeat to Porto on Wednesday.
Celtic allowed two goals to Hapoel Be'er Sheva but the Scottish side still qualified for the UCL group stages on aggregate, 5-4.
Roma's Champions League campaign is over before it began, losing 3-0 to Porto and earning two red cards in the process.