Papiss Cisse's close range header with 19 minutes remaining breathed life into an edgy encounter at St James' Park, but despite constant pressure they were unable to find the second goal that would have sent them through.
That search left them exposed at the back, allowing Eduardo Salvio to level in injury time.
The late goal meant Newcastle failed to join Barcelona and Spartak Moscow as the only teams to defeat the Portuguese League leaders in Europe this season.
Despite the defeat, Newcastle manager Alan Pardew remained upbeat and said he had no regrets at the manner of their exit.
"They are a good side, you can't let them get the lead against you," he told Britain's ITV.
"We defended well in the first half, kept it tight, looked to try and nick a goal and almost got one just before half-time.
"The second half we were going to... see if they could cope and they couldn't really, we had two or three big chances at one-nil.
"But I can't ask for anything more... from the players, I thought they were excellent tonight."
Chances were few and far between in the first half, with the best falling to Benfica's Nicolas Gaitan, whose goalbound shot was blocked by Massadio Haidara after keeper Tim Krul had lost possession on the edge of his goalbox.
Cisse had a goal rubbed out for offside late in the half, and suffered the same fate soon after the hour mark following a flick by Shola Ameobi.
He was not to be denied minutes later after the returning Hatem Ben Arfa robbed Nemanja Matic and fed Ameobi, whose chip from the byline gave Cisse an easy finish.
Despite throwing men forward as full-time approached, Newcastle were unable to find the break they needed, and always looked vulnerable at the other end.
They were finally undone in the 92nd minute when Rodrigo teed up Salvio for a smart finish.
The draw for the semi-finals is on Friday.
