Koeman endured a rough start to life with the Saints, when a number of his key men left during his first transfer window, but the Dutch boss says that the experienced trio helped to settle the players during a potential disruptive period.
"I came to the club and I feel at that time difficulties because we had to sell a lot of players," he said.
“I think the one good thing what we did was with Jose, but also with Kelvin (Davis), with Steven Davis, was inform the players about the strategy of the club, about the way we like to play.
“For sure to say to them, we will keep quality, we will bring in good new players, and of course then you have to wait.
“But from that start, that pre-season in my first year, I think it was difficult but these players is important players, we show ambition to the rest of the squad. That was important and little by little we did well, we had good results.
“The new signings showed the qualities and everybody was happy.”
Koeman has kept Kelvin Davis, Steven Davis and Fonte at the club to this day, and they all played for him in Southampton's latest draw against Leicester City.
Kelvin Davis was required to play in goal in the game, at the age of 39, while Fonte and Steven Davis played in their usual roles of centre-back and central midfield respectively.
They are all some of Southampton's longest-serving players, with Fonte and Kelvin Davis having stuck with the club since their days in League One.
The Saints have risen rapidly since then, but Koeman obviously feels that all three still have a part to play in the future of the club.
Southampton are currently in eighth place in the Premier League table, with their next fixture coming against Liverpool on Sunday.