Emery has won two out of four games this season after replacing Arsene Wenger as manager in the summer.
And O'Leary, the club's record appearance holder, believes the Gunners' rivals will struggle to better their sixth-placed finish last season because their rivals haven't declined.
"I look at the five teams that finished ahead of us, I don't think they've got any worse," O'Leary told Goal.
"I think it was going to be a tough job for whoever was going to come in here.
"If this manager gets into the top four, I think it's been a great achievement."