Rovers had left themselves with plenty of work to do after slumping to a 2-0 defeat in the first leg in Greece, with boss Mark Hughes pairing Roque Santa Cruz with Matt Derbyshire in attack for the Ewood Park return.
The task for Blackburn became that much harder just 17 minutes in as Panagiotis Katsiaros' ball into the box fell nicely for Cleiton to bury a shot past the stranded Brad Friedel.
David Bentley led the Rovers charge after that setback and just before the half-hour mark his free-kick was headed narrowly over by Christopher Samba.
Just as Larissa looked to be going in at the interval in total charge, Rovers were awarded a penalty for a foul on David Dunn.
Derbyshire's initial effort was saved by Stefanos Kotsolis, but the referee ordered a retake and the England Under-21 international sent the keeper the wrong way second time around to make the score 1-1 on the night.
Six minutes into the second half Rovers had reduced the aggregate deficit to 3-2 as Bentley's ball in from the right reached Stephen Warnock and he fired home past Kotsolis.
Soon after Hughes brought on Morten Gamst Pedersen to try and complete a complete turnaround, but the Larissa backline held firm to protect their advantage.
Fourteen minutes from time Samba's header caused problems in the visitors' defence, but they eventually got the ball clear.
The giant centre-back was playing up front by this stage and, although he continued to be a nuisance for the Greek defence, Larissa held out with some ease to end Rovers' European hopes.