TNS earned a creditable goalless draw in the first leg but fell behind after only eight minutes tonight when Walid Atta scored from Jere Uronen's corner.
Thomas Sorum made it 2-0 before half-time and Alvaro added a late third for the Allsvenska outfit.
Northern Irish side Linfield also bowed out of the competition 3-0 on aggregate at the hands Cypriot champions AEL Limassol.
David Jeffrey's men were always up against it in the second leg at Windsor Park following their 3-0 defeat in Cyprus last week.
They clawed back some pride with a resilient display but could not break down a stubborn AEL rear-guard, resulting in a 0-0 stalemate.