The inspirational midfielder and his brother Kolo, the centre-back, will head to South Africa to play in the African Nations Cup with Ivory Coast next month.
The Toures, and particularly Yaya, were badly missed when the tournament was last held last season with their absences coinciding with a spell of patchy form.
City expect the brothers' last game before their departure to be the FA Cup third-round tie against Watford on January 5.
It is possible they may not be an action again for City until the home Barclays Premier League clash with Chelsea, seven weeks later, on February 24 - although that depends on results in Africa and the FA Cup.
Platt said: "I'm not too sure how many games he is gone for but it's something we have known about and will have to deal with.
"We lost him last year and won the league. The kind of player he is, it would be more beneficial to have him and it's similar with Kolo.
"But we will get on with it. It's like an injury - you want the full complement to choose from.
"We have a dressing room full of quality players and we have to cope with it."
There has been speculation City could look to strengthen their squad during the January transfer window, to freshen their title challenge and offset the loss of the Toures.
But Platt has played down that possibility.
He said: "The type of player that would benefit one of the top clubs, not just Manchester City, is likely to be involved already at a top club who are chasing honours and wouldn't want to let them go.
"I wouldn't be surprised if we didn't do any business."