The Toon trailed 3-1 going into the second leg at St James' Park but were unable to win by two clear goals, conceding late to be held to a 1-1 draw and losing 4-2 on aggregate.
Papiss Cisse, who had two earlier goals ruled offside, edged Newcastle ahead in the 71st minute when he headed home Shola Ameobi's cross from close range.
The chances kept coming, especially as Newcastle chased a second goal but in the end it was their downfall as Benfica pounced in injury-time with substitute Rodrgio picking out Eduardo Salvio who slotted home at the death.
2012/13 UEFA Europa League quarter-final - second leg
St James' Park, Newcastle-upon-Tyne - 52,157