Napoli dominated possession and twice struck the crossbar without ever putting goalkeeper Milan Borjan under sustained pressure in the Serbian capital on Tuesday.
Ancelotti is confident his team can make up for the dropped points but was less positive about Red Star's method of negotiating the final stages.
"It was inevitable that the last 15 minutes would be different," Ancelotti told Sky Sport Italy.
"They are professionals at time wasting and diving. They play tight and they are always looking for a foul.
"But that's not the problem. We should have scored earlier.
"It was close, we just lacked the final spark. We made little mistakes in passing and shooting. We were unlucky too."
0 - This only the third match in the history of modern Champions League in which Napoli haven't score. Caged.— OptaPaolo (@OptaPaolo) September 18, 2018
While tougher tasks are still to come, the experienced Ancelotti – three times a Champions League winner as a coach – warned against overreacting to Tuesday's result.
"We didn't win an important game, but we shouldn't be so negative," he said.
"There are still five games to go and we can beat anyone. We didn’t score, it's a pity, but we were very close."