The arrival of Arouna Kone from Wigan Athletic has cast doubt over the Croat's future.
But Osman told the Liverpool Echo: "Any player can have a tough season or a dip in form. The one thing you can't let up is your commitment and you can always give that.
"He showed what he was capable of in that first three or four months when he came over, and we haven't got anything to complain about what he did last year because he always worked as hard as he could for the team. When you ask someone to go over that white line and they give you everything you can't really complain.
"Looking at the bigger picture - the most successful clubs are the ones who have an abundance of choices in strikers and we're now getting there with quite a few options. It's better for us."