Trailing 3-2 from the first leg, injury-ravaged Boro battled hard to overturn the deficit but eventually succumbed to a late Pedro Barbosa strike.
Steve McClaren was without nine senior players, including experienced European campaigners Jimmy Floyd Hasselbaink, Mark Viduka, Michael Reiziger, Ray Parlour and Gaizka Mendieta, but had the better of the first 45 minutes at the Estadio Jose Alvalade.
With less than two minutes on the clock Stewart Downing broke down the left wing and his cross just missed Joseph-Desire Job's head.
The visitors had to survive a penalty appeal when Liedson fell in the penalty area, before Mark Schwarzer gathered a tame Beto free-kick.
The best opportunity of the half fell to Szilard Nemeth after Job beat Sporting goalkeeper Ricardo to a ball over the top, but Nemeth found Rui Jorge on the goal-line and the defender hacked clear.
Sporting appeared happy to keep hold of possession in midfield and did not look to create much, although Schwarzer had to parry a drive from on-loan Newcastle midfielder Hugo Viana.
Seconds before the interval Ricardo spilled a Downing cross, but managed to recover and produce a stunning save to deny Stuart Parnaby.
Five minutes after the break Ricardo presented Boro with another great opportunity when his mis-hit clearance found Nemeth.
The Slovakian crossed to present strike-partner Job with a straightforward chance, but somehow he pushed the ball wide of an open goal from just six yards out.
The let-off seemed to spark the home side into action and minutes later Douala picked out Barbosa, who saw his drive saved by Schwarzer.
The Australian kept Boro in it again after 77 minutes when he palmed Liedson's flick over the crossbar, before tipping Viana's free-kick to safety
However, Schwarzer was powerless to prevent Barbosa stroking Douala's pull back home in the final minute to clinch a 4-2 aggregate success for the Portuguese side.