The Magpies only confirmed their safety with victory at QPR last weekend, and the French defender feels that such a position is unacceptable for a club of Newcastle's size.
Yanga-Mbiwa, one of five permanent French signings in January for Newcastle, thinks that a place between eighth and sixth would be appropriate for the club.
"First of all, a team like Newcastle should not be in a situation where we need to worry about relegation," Yanga-Mbiwa told the Newcastle Chronicle.
"It's good that we have made sure a great club such as this remains in the Premier League. It would obviously have been nice to succeed a little bit earlier, but it's better later than ever.
"It is natural for me to look forward. That is normal. You have to prepare for the months and years in front of us. We must make sure we play better.
"We know we can play better next season. I am definitely hoping to get into the top 10, climb up that league.
"I think we can go for between eighth and sixth. I don't think that's over-estimating us. We should be able to go into the top positions and compete with the best."