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In the second game of Group A, the Giallorossi were unable to build on their winning start last week against Young Boys - as neither side could break the deadlock in a fairly turgid game in the Italian capital.
The Giallorossi undoubtedly had the better chances, however: with Henrikh Mkhitaryan hitting the bar in the first half, and Edin Dzeko just inches away from tapping Pedro's cross into the unguarded net late in the second.
But the visiting Bulgarian side held firm throughout and indeed occasionally looked dangerous on the counter-attack - with Pau Lopez needing to be alert more than once to deny Ali Sowe.
In the closing stages, however, it was CSKA goalkeeper Gustavo Busatto who was by far the busier - as he stood tall to deny both Dzeko and Lorenzo Pellegrini to preserve the clean sheet.
Paulo Fonseca's side are back in action on Sunday - Fiorentina are the visitors to the Olimpico.
The following Thursday they host Romanian side Cluj in their third group game of the Europa League.
ROMA 0-0 CSKA SOFIA
ROMA (3-4-3): Pau Lopez; Fazio, Smalling (Juan Jesus), Kumbulla; Peres, Cristante, Villar, Spinazzola (Karsdorp); Mkhitaryan (Pedro), Perez (Pellegrini); Mayoral (Dzeko)
Unused subs: Boer, Mirante, Ibanez, Veretout, Zalewski, Milanese
CSKA SOFIA (4-2-3-1): Busatto; Vion (Turitsov), Antov, Zanev, Mazikou; Youga (Beltrame), Gefferson (Tiago); Sinclair (Henrique), Sankharè (Ahmedov), Yomov; Sowe
Unused subs: Evtimov, Carey, Keita, Penaranda, Galabov
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