I did it with the help of HttpClient inplace of WebClient. Following few lines will do magic. :)
HttpClient hc = new HttpClient();
hc.BaseAddress = new Uri(annotation_url.ToString());
HttpRequestMessage req = new HttpRequestMessage(HttpMethod.Post, myUrl);
HttpContent myContent = req.Content = new StringContent(myJsonString, Encoding.UTF8, "application/json");
var response = await hc.PostAsync(myUrl, myContent);
//Line for pull out the value of content key value which has the actual resposne.
string resutlContetnt = response.Content.ReadAsStringAsync().Result;
DataContractJsonSerializer deserializer_Json = new DataContractJsonSerializer(typeof(MyWrapperClass));
MemoryStream ms = new MemoryStream(Encoding.UTF8.GetBytes(resutlContetnt.ToString()));
AnnotateResponse = deserializer_Json.ReadObject(ms) as MyWrapperClass;