The Dutchman was handed the job of rebuilding the Saints squad after a summer of upheaval, and he now believes that there are not many teams in the English top flight better than Southampton.
Asked if he thought they could maintain their challenge for a top-four place this season, Koeman is quoted by the Northern Echo as saying: "We can keep this, I'm not afraid about the situation. If I look at the rest of the teams, I don't think a lot of them are better than Southampton.
"I think we have gone under the radar. Maybe some people are very surprised but from the start of the season I saw what I had and I had belief, belief in the players and their spirit.
"Okay, maybe not to be second in the league at this moment, but we have good players and we play good football and everybody enjoys how we play. This is very important."
Koeman's men travel to Hull City this afternoon in search of yet another Premier League win.