The Cherries have had a gruelling fixture schedule to start the season and are yet to win in the Premier League, but ground out a dogged goalless draw at home to Chelsea on Sunday.
"It is always a good result, even if this is not currently the best version of Chelsea," Onuoha told BBC Radio 5 Live's Football Daily podcast. "They showed signs to make you believe they will be OK.
"A Bournemouth fan on the radio made the point they want to see good attacking football and under Andoni Iraola they are doing that, so overall they are not happy.
"It is not that they are happy about not winning games - but he was talking about finishing between 12th and 16th, and they are not a million miles away from that."
Telegraph journalist Luke Edwards agreed, saying Bournemouth "have a bit about them" and pinpointing Dominic Solanke as crucial to their hopes this season.
"He has come on brilliantly," Edwards said. "Bournemouth have had a cruel set of fixtures to start the season and I think they will be OK."