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 it 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 host's net.
The excellent Muriel was involved again soon after as he fed Matteo Pessina into the box, but Ospina saved at his feet and Rafael Toloi hopelessly shot wide a few minutes later following a clever one-two.
Muriel then wasted a decent chance of his own late in the half, blazing over from just inside the area after cleverly evading Kalidou Koulibaly.
Ospina remained busy at the start of the second period as he first rushed out to thwart Muriel, before holding on to Joakim Maehle's excellent header from a corner just past the hour.
Napoli's midfield presence diminished considerably as it lost Diego Demme and Lorenzo Insigne in quick succession to knocks, with Atalanta's dominance increasing as a result.
But Robin Gosens missed a glorious chance as he headed wide 13 minutes from time and that proved to be their final opportunity.