Ferdinand has already begun his ban for a missed drugs test and it was widely predicted that Manchester United would struggle to cope in his absence in the heart of their defence.
However, the Republic of Ireland international believes Brown's return from long-term injury will considerably soften the blow of losing Ferdinand.
United's rearguard looked creaky in last week's 3-2 home win over Southampton, but O'Shea backed Brown to forge a strong partnership with Mikael Silvestre.
"It just so happened that Rio's situation coincided with Wes coming back to full fitness," stated the 22-year-old.
"So I don't think we'll miss Rio as much as people think."
