The Magpies opened the scoring through Papiss Cise, who also hit the woodwork on two occasions, before conceding three times at Estadio da Luz in Lisbon but Pardew is confident of reversing the result in the Europa League quarter-final second leg at St James' Park next week.
"Of course it is possible, anything is possible. If we can put Benfica under pressure at home, pressure can do funny things to you," said Pardew.
"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."