The Italian side entered the game with the knowledge that anything other than a loss would see them qualify for the round of 16, while Ajax needed all three points to avoid finishing third and dropping to the Europa league.
Ajax forward Klaas-Jan Huntelaar had a penalty appeal turned down in the 68th minute after a clumsy challenge inside the box from defender Cristian Romero, but both the referee and VAR agreed it was not a penalty.
Dutch international Davy Klaassen found himself free in the penalty area in the 70th minute, but saw his shot saved via the feet of Gollini.
"I should have scored," Klaassen said of his missed chance. "But it was a difficult game, they didn't come to score but defended well, they were very compact and we created too few chances."
Atalanta have qualified for the knockout stage for the second consecutive season.