The Magpies initially had the upper hand in Lisbon thanks to a 12th-minute close-range strike from Papiss Cisse, who subsequently hit the post.
But the hosts equalised after 25 minutes when Rodrigo finished from a Tim Krul parry, and after Cisse struck the woodwork again with a chip early in the second half, Benfica took control of the tie.
First, Davide Santon's poor attempted back-pass allowed substitute Lima to round Krul and make it 2-1 in the 65th minute.
Then, six minutes later, Oscar Cardozo scored a penalty after Steven Taylor was penalised for a handball.
Pardew admitted his team now face a tough task in trying to keep their European campaign alive, but stressed his belief that they are capable of emerging from next Thursday's return leg at St James' Park with a place in the semi-finals.
"We need to score first I think to have a realistic chance in that game," Pardew said.
"But I think we showed that we can cause them problems. Of course it is possible (to still win the tie), anything is possible.
"If we can put Benfica under pressure at home, pressure can do funny things to you. You could score two quick goals and suddenly the tie could have a very different feel."
- Sports & Recreation
- Papiss Cisse
- Tim Krul
- Davide Santon