The Toon defied all odds last season to finish fifth in the Premier League and Ameobi said that the same finish would be even tougher this year.
"It's certainly going to be really difficult to replicate what we did last season," The Journal quotes Ameobi as saying.
"Just look at teams such as Liverpool and Chelsea - I can't see them doing as badly this time in terms of where they finished in the league last season, so we are going to have to raise the bar again.
"Certainly, as I look back at my career with Newcastle, to [finish fifth] this time would be our biggest ever achievement."
The 30-year-old has scored 50 league goals for Newcastle.