Injuries and suspensions have ravaged Ince's ranks throughout the season and with Gary MacKenzie, Bradley Orr, Angel Martinez and Ricardo Fuller all already out of the weekend's clash with Burnley, Osbourne's injury adds further woe.
The 26-year-old, formerly of Aston Villa, has already missed a chunk of the season through injury, which has restricted him to 14 appearances so far.
"Ozzy is a massive blow because we've just got him back," said Ince.
"It was innocuous because he's made a tackle and then he tried to stretch again and we thought it might just be a little ache because of the pitch, but we found out it was grade two (tear).
"Angel is suspended and if we lose Cathers (Craig Cathcart) then we might have a makeshift defence again. It's hard sometimes, people need to realise if you go through all our games and the formations we've had to use players in...it's been a tough 20 games.
"The lads have done ever so well to play in positions they're not accustomed to. E ventually we want a balanced team where players play in the positions they're supposed to."