Aside from his goal against Everton at the weekend, Carrick has done little this season to impress. With Ljajic arriving, Hargreaves returning, and Gibson pushing his case for the occasional first team appearance, one may question when Carrick would be used in a central midfield consisting of Anderson, Scholes, Giggs, Fletcher, Hargreaves, Ljajic and Gibson, all competing for 2 positions.
Perhaps the answer is to only use him alongside a more defensive midfielder, such as Hargreaves, Gibson or Fletcher. Carrick's big strength is his creative passing, and the defensive forced on him when paired with an attacking midfielder means that he has to be cautious about putting some effort into defending, meaning that he can't fully optimize his game. Playing him alongside a defensive mid would cut out that responsibility, allowing him to focus on his attacking strengths.
Maybe both of those suggestions are not the answer, and Carrick may find some form in the near future, but if this current slump continues, then I feel that action must be taken.