The south-coast outfit handed Osvaldo a two-week suspension last Thursday in response to an "incident at the club's training ground".
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"It has been eventful, obviously, and what happened wasn't nice at the training ground, but I am man enough and I have moved on and I hope everyone can move on and focus on what is important, which is Southampton, the club and winning games of football," Fonte told the club's official website.
"There is no problem with me – I am fine, so I just want to keep playing.
"This group is very strong mentally and the togetherness is there. We know each other really well and know what we are all capable of."
Southampton club captain Kelvin Davis appeared to aim criticism at Osvaldo, who has been linked with a move away from St Mary's, following Saturday's FA Cup win over Yeovil Town.
Davis said: "We've said for a long time that we have always had a good team spirit and a good changing room. That can't change and if anyone doesn't want to be involved in that then they are not welcome."