Gian Piero Gasperini's men were in control for much of the game and created the best chances of the match, but they ultimately had to settle for a draw ahead of the return leg in Bergamo next week.
Luis Muriel was Atalanta's danger man, proving a real nuisance to Napoli as he offered a threat in front of goal and also proved an able creator, though Ospina in the home side's net stood firm.
Napoli might have been expected to produce an improvement after the interval but still they struggled to craft openings of their own, consigning them to an underwhelming 0-0 first-leg draw.
Although Napoli looked bright at first, Atalanta soon became the dominant force and went close to a fluke early lead when Muriel's wicked free-kick delivery from the left drew a desperate save from his compatriot Ospina in the hosts' net.
Napoli's midfield presence diminished considerably as they lost Diego Demme and Lorenzo Insigne in quick succession to knocks, with Atalanta's dominance increasing as a result.