Having already won Group E, the Giallorossi named a rotated side - and while they dominated possession for almost the entire match, they struggled to create many clear-cut opportunities.
Astra, hoping to secure second spot in the group, needed a win to be sure of doing so - but in the end a draw proved more than enough for them, after Viktoria Plzen beat Austria Wien elsewhere on the night.
The biggest moment of note came in the second half, as Astra forward Denis Alibec had a goal (correctly) ruled out for offside.
Roma had more chances but few really threatened: substitute Edin Dzeko going closest as he headed over from a late corner.
The Giallorossi will find out their opponent for the last-32 of the competition on Monday.
With qualification already assured, Spalletti used the opportunity to give other members of his squad a chance to impress - with Moustapha Seck making his debut for the club and Thomas Vermaelen making his first start for a number of months.
Francesco Totti led the attack alongside Juan Iturbe, while there was another chance to impress in midfield for Gerson.
15': First sight of goal for Roma - as Totti blasts over from a long distance free-kick.
34': Iturbe goes for a low drive from range - it's just wide of the far post but not wide enough for Totti to turn in...
44': Something for the home crowd to cheer as Alisson is forced into two smart saves.
50': Astra Giurgiu have the ball in the net through Alibec ... but it's disallowed for an obvious foul in the build-up.
66': Seto forces another save from Alisson, who gathers the shot relatively comfortably.
87': CLOSE! Iturbe rifles in a corner that Dzeko heads fractionally over the crossbar!
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To follow...
The Giallorossi now have three Serie A engagements to complete before the winter break - they host AC Milan on Monday, before travelling to meet league leaders Juventus on Saturday week.
Their final game of the year, against Chievo, is at the Stadio Olimpico on Thursday 22 December.
Astra Giurgiu: Lung, Oroș, Săpunaru, Fabrício, Nicoară, Seto, Stan, Teixeira, Lovin, Alibec, Budescu
Roma: Alisson; Peres, Vermaelen, Jesus, Seck; Emerson (Marchizza), Gerson, Strootman (Nainggolan); Iturbe, Totti (Dzeko), El Shaarawy.
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