The centre-half sported a black eye after being headbutted by Osvaldo, who was loaned out to Juventus last month after failing to settle on the south coast following his move from Roma.
Southampton's club-record signing scored just three goals in 13 appearances before departing only five months into a four-year deal, and Fonte believes the decision to release Osvaldo was the right course of action.
"There have been a couple of text messages, apologising and stuff, but some things take time to heal," the Portuguese defender said.
"The spirit has always been fantastic. We have known each other for a long time and one of our best assets is the team spirit.
"Yeah, he left, obviously he left for a reason, and it was for the best for the team and the club.
"We move on, I've moved on and he has surely moved on as well, so everything is all right."
Asked if he had any input in Osvaldo's exit, Fonte said: "Me? No. What can I say?
"The boss is Mauricio Pochettino and he knows what happened and decided that it would be best for the group for him to move on."
Fonte was disappointed that Southampton twice failed to hang onto leads against Stoke in their 2-2 draw at St Mary's on Saturday, blaming "sloppy" defending for the Potters' two goals.
"It was a disappointing day," Fonte added. "This is one of those days when you are ahead, when you are in a winning position and you need to close up and just not concede any more.
"We were twice in winning positions and twice conceded sloppy goals, in my view.
"It was frustrating not to get three points at home. At the end, we went to the dressing room feeling a little bit like we could have done more than just a draw."