Ancelotti's side are top of Group C and host the section's bottom side Red Star Belgrade on Wednesday, the same day Paris Saint-Germain welcome Liverpool to the French capital.
Napoli appear well-placed to reach the next round and will seal qualification with a win over Red Star if PSG do not beat Liverpool.
And Ancelotti, a three-time Champions League winner, made his expectations clear at a pre-match news conference.
"Well I think many people have been surprised seeing Napoli competing with very high profile teams," the Italian told reporters.
"We have been a real surprise in this group and I think those same people would be even more surprised if we manage to go through the next stage.
"If we don't qualify instead we can call ourselves... a*******.
"At this stage of the competition I truly believe that if we don't qualify we should call ourself a*******."
While Napoli are thriving, sitting second in the Serie A table, Ancelotti's old club Bayern Munich are struggling in the Bundesliga.
Ancelotti was sacked by the German giants last term and pressure is growing on Niko Kovac with Bayern fifth in the table, nine points behind leaders Borussia Dortmund.
"I think Bayern are experiencing the same problems I did," Ancelotti added "I'm always on the manager's side.
"I wish Kovac can do his best there and all the best to him in general. For me it wasn't easy - I truly hope is going to be easier for him."