The Saints finished eighth last term but have since lost manager Mauricio Pochettino to Tottenham Hotspur and five of their key players this summer.
It has been suggested that new boss Koeman may struggle to keep his weakened St Mary's squad in the top flight, but the Dutchman is adamant that Southampton are still strong enough to avoid a dramatic fall from grace.
"For me, eighth to relegation is a lot of positions," Koeman told reporters. "I don't think that will happen - we lost a lot of good football players but brought in some new ones.
"The pre-season was difficult, but it's been difficult for everybody. Until the end of August we can bring in more changes but every team has that problem.
"We are prepared and I believe in the qualities and our ambition and that we can do a good season."