The Magpies opened the scoring at the Estadio da Luz through a 12th-minute strike from Papiss Cisse, who subsequently hit the post.
But the hosts equalised on 25 minutes when Rodrigo finished from a Tim Krul parry, and after Cisse struck the woodwork again with a delicate effort early in the second half, Benfica took control of the tie.
First, Davide Santon's poor attempted backpass 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 in the area.
Reflecting on his team's efforts, Pardew said: "We are disappointed with the result because of the performance level. In some parts of the game we played very, very well.
"I thought we probably had them just where we wanted them just before their second goal and then it is two poor goals on our part.
"There was obviously a mistake for the first and then with the second Steven is so unlucky.
"It looks like he has caught his boot laces in his studs and that it has affected his jump (when the ball struck his arm), and we have ended up gifting them a third."
Pardew was eager to emphasise that the blame for errors was collective.
"We have to accept mistakes as a team," Pardew said. "There is no (individual) responsibility.
"We had a fantastic opportunity to take the lead again in the second half. The post has denied us twice.
"I can't really say anything more. I was overjoyed with the performance but not the result, and that probably sums up my feelings.
"I thought on another given day we could have got a much better result, for sure.
"Certainly the third goal was really unlucky and that goal just gives a nice cushion for Benfica."
Pardew admitted his team now face a tough task in trying to keep their Europa League campaign alive, but stressed his belief they could emerge from next Thursday's return leg at St James' Park with a place in the semi-finals secured.
"I think at our place the away goal could come into it," Pardew said.
"We need to score first I think to have a realistic chance in that game. But I think we showed enough tonight that we can cause them problems.
"They are a good side, there is no doubt about that. But for long periods in that game we were comfortable.
"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. I've seen enough and been in enough European ties to know that."
Benfica coach Jorge Jesus made it clear he also feels the tie is far from over.
Asked if he thought the quarter-final had been decided with this evening's result, Jesus said: "No. Newcastle showed tonight they are a strong team and they are even stronger at home and more aggressive.
"It (the second leg) will be an open match, but we are ahead.
"We had a really great match tonight. There was a bit of everything - missed chances, taken chances, a lot of emotion.
"Newcastle started well but we never worried. We have worked hard all week and we managed to turn the game around with the help of our supporters."