After winning the first leg 3-1 at White Hart Lane last week, Jorge Jesus's team appeared to be cruising towards the last eight when Ezequiel Garay scored in the first half at the Estadio da Luz.
But Nacer Chadli struck twice in quick succession late in the second half to give Spurs hope of forcing extra-time.
Benfica barely managed to hold out before Rodrigo Lima's penalty in stoppage-time sealed a 5-3 aggregate success which secured the Portuguese club's spot in Friday's quarter-final draw.
Sherwood had accused Jesus of lacking class after the Benfica boss taunted his counterpart on the touchline at White Hart Lane, holding up three fingers to signal his side's third goal.
But it was another first leg menace, Benfica's Luisao who was a more pressing concern for Sherwood, whose plans were disrupted by injuries to 11 first team stars.
Luisao had been the surprise match-winner with two goals at White Hart Lane and the defender's aerial prowess troubled Tottenham again in the early stages when he headed just over.
Soldado wasted two chances to give Tottenham a lifeline when the out-of-form Spanish striker scuffed a woeful shot wide and then poked over after hesitating too long.
It wasn't long before Spurs were made to pay for that profligacy.
Benfica, beaten by Chelsea in last season's Europa League final, had scored in each of their last 25 matches in all competitions and they extended the run in the 34th minute.
Eduardo Salvio showed impressive footwork to skip past Aaron Lennon and clip a cross towards Garay, who timed his run to bullet a header past Brad Friedel from seven yards out.
That prompted a disconsolate shake of the head from Sherwood, who was watching from high in the stands after several weeks of manic antics on the touchline.
But to their credit, Sherwood's players, criticised by their manager for lacking spirit after a recent thrashing at Chelsea, refused to surrender and staged a strong comeback to avoid a fourth successive defeat.
Chadli started the revival when he equalised with a powerful low shot from the edge of the area in the 78th minute.
And the Belgian winger struck again one minute later, swivelling to sweep home Harry Kane's knock-down.
Benfica were shell-shocked and the visitors poured forward in search of the third goal which would have forced extra-time.
They appealed in vain for a penalty when Kane was bundled over by Miralem Sulejmani and moments later it took a fine save from Jan Oblak to deny Gylfi Sigurdsson's header.
As Tottenham threw bodies forward they were caught on the break and Sandro chopped down Lima, who picked himself up to stroke home the penalty and finally settle the tie.
Source : AFP
Source: AFP