I was disappointed that the story didn't have a rising action or climax or any kind of emotional pull - stuff just kind of happened. I also thought that the fact that there were basically eight protagonists kind of meant that none of them were developed to the point where I felt any kind of emotional attachment towards them. I mean, the acting was great and the movie was shot well, but when I walked out of the theater, I didn't really feel anything other than indifference.l

I believe a quote from this review sums up my feelings perfectly:

http://www.theatlantic.com/entertainment/archive/2011/09/in-contagion-many-actors-but-only-one-star-disease/244777/ wrote:

Much as it pains me to say it, the movie could have used a firmer emotional and narrative rationale—a lesson, even—beyond "wash your hands often and hope you're lucky." Lacking that, the film resembles its viral subject a little too closely: an intricate, formidable mechanism with no evident purpose. For all the craft that went into it, Contagion is ultimately beyond good or bad, beyond criticism. It just is.