The Bundesliga club's director of sport Rudi Voller admitted the draw could hardly have been more difficult, although they will nevertheless accept the challenge, which he feels is both attractive and manageable.
"Benfica played a great group stage and are leading the way in Portugal at the moment," he said.
"This is truly a tough task, but in good form, we certainly have a chance and I expect it to be a clash between two sides on a par with each other."
Benfica finished third in their Champions League group behind Barcelona and Celtic.
Stuttgart got what appears to be an easier draw against Belgian side Genk.
"We can be happy - they are attractive opponents who were playing in the Champions League last season," said the club's director of sport Fredi Bobic on vfb.de.
"They have a small but fine stadium and it's a brutal cauldron where things really are hostile.
"It won't be easy, but we are not unhappy because it's a do-able draw."
Borussia Monchengladbach have a tough clash with Lazio, the side which pipped Tottenham to group victory and have Germany international Miroslav Klose among their ranks.
"This is an incredibly attractive draw for us," said their director of sport Max Eberl.
"The games against Lazio are going to be great challenges."
Hannover, the Bundesliga's fourth side still in the Europa League, can also expect two challenging matches against Russian outfit Anji Makhachkala with the first leg being staged in Moscow in mid-February.
"I see it as an advantage that we play the second leg with our fans behind us at home," said coach Mirko Slomka on his club's website.
"Anji are a huge challenge for us."