The Saints lost a number of key players last summer including captain Adam Lallana, left-back Luke Shaw, experienced striker Rickie Lambert and versatile defender Calum Chambers while manager Mauricio Pochettino left for Tottenham.
Dutch tactician Koeman took over from the Argentine and suggests that everybody involved with the south coast club was a little scared at what might happen but their current position of seventh suggests that the players have banded together under duress at St Mary's.
"Everybody was afraid because we had to make a lot of changes in the team," Koeman said.
"But I think the quality of the players that we brought in were good, at a good level. I think the rest of the players had really a good aspiration and ambition to do a good season, to play a good season at a good level.
"Now we are fighting for a high position in the table."