The Magpies got off to a great start and Papiss Cisse gave them a 12th minute lead but the unfortunate striker went on to hit the woodwork twice and Benfica surged back, finding the net through Rodrigo, Lima and Oscar Cardozo.
Lima's goal followed a bad back-pass from Davide Santon but Pardew refused to criticise his side and felt they deserved better.
And, asked if Newcastle can still advance, Pardew said: "Of course it is possible, anything is possible. If we can put Benfica under pressure at home, pressure can do funny things to you.
"I think at our place the away goal could come into it. We need to score first, I think, to have a realistic chance in that game, but I think we showed enough tonight to prove 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.
"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.
"I thought we probably had them where we wanted them just before their second goal and then it is two poor goals on our part.
"We are disappointed with the result, because of the performance level. In some parts of the game we played very, very well."
Asked if he thought the tie was over, Benfica coach Jorge 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."