Paulo Bento's Portugal were without star forward Cristiano Ronaldo due to the injury problems that were a constant concern during Real Madrid's end-of-season run-in.
And their lack of attacking invention showed in Oeiras as they struggled to break down a well-organised Greece side.
However, it is Greece who made the headlines for unwanted reasons, defender Papastathopoulos substituted after pulling up injured late in the first half with an apparent muscle problem, leaving his hopes of participating in the World Cup in doubt.
Even without the Borussia Dortmund defender to shackle them, Portugal never looked like breaking the deadlock, and Bento will hope his side can show more in front of goal in their final two pre-tournament friendlies, against Mexico and the Republic of Ireland.
Greece's concerns are likely to be focused on the fitness of Papastathopoulos prior to meetings with Nigeria and Bolivia in their last two warm-up games.
Portugal started brightly and could have taken the lead in the first minute when Greece goalkeeper Orestis Karnezis was forced into action as Eder met Nani's right-wing cross with a diving header.
The hosts continued to look the more threatening and six minutes later they were again denied by Karnezis, who tipped Bruno Alves' header over the crossbar from Miguel Veloso's near-post corner.
Bento's men were unable to capitalise on their early dominance, though, and the game soon lost its spark, with both sides struggling to create opportunities.
Greece were then dealt a blow in the 40th minute as Papastathopoulos limped off to be replaced by Vangelis Moras.
Portugal continued to find joy down Greece's left flank, and came close to netting an opener when Nani broke free down the wing early in the second half, but his low ball across the six-yard box failed to find a team-mate.
That missed opportunity summed up Portugal's frustration, and they could have lost the game five minutes from time, but goalkeeper Beto kept out Ioannis Fetfatzidis' low effort after the substitute had worked his way into the box from a corner.
Ricardo Costa's deep cross then hit the top of the crossbar in the final minute of injury time as Portugal were left stifled in a game that offered little as a spectacle.
