Papiss Cisse's second half goal reduced the arrears in the tie, but Eduardo Salvio's injury-time strike ended Newcastle's hopes of pulling off a comeback victory.
Cisse also had two goals rightly ruled out for offside as the home side battled to overturn their 3-1 deficit from the first-leg in Portugal, but Benfica did enough to reach the last four.
Newcastle made a shaky start to the game and Benfica went close to scoring after just three minutes when Andre Almeida fired over a cross from the right and Rodrigo Lima saw his backheel flick saved by the legs of Tim Krul.
Benfica continued to call the tune in the early stages and Krul almost gifted them a goal on 28 minutes when he came out to the edge of the box to collect a ball but knowing he couldn't handle it, dropped it at the feet of Lima. The Brazilian striker then picked out Nicolas Gaitan, who saw his goalbound shot cleared off the line by Massadio Haidara.
The Portuguese side went close again on 36 minutes when Ola John got to the byline and hung up a cross to the far post to Eduaro Salvio, who saw his header fall just wide of the target.
Newcastle were struggling to make any inroads in the final third, but they had the ball in the net on the stroke of half-time when Papiss Cisse turned home Gael Bigirimana's cross from close-range. However, the home side's celebrations were cut short by an offside flag.
The hosts improved in the second half as substitute Shola Ameobi provided some support for Cisse in attack.
Cisse had the ball in the net again on 66 minutes when he volleyed home Ameobi's flick-on, but again the strike was ruled out for offside.
Newcastle finally did make the breakthrough five minutes later when Ameobi crossed for Cisse to head home from close range to send the home fans into raptures.
Newcastle threw everything at Benfica as they went in search of the second goal which would send them through, but Benfica's defence stood strong to keep them out.
Benfica then caught them on the break deep into injury-time when substitute Rodrigo crossed for Salvio to sweep the ball home and break Newcastle's hearts.