I have synced my contacts from my phone but I can only see few of them on the Web App.

My Contacts syncs those contacts which are saved on Outlook, Gmail, Hotmail, your internal phone memory etc. Contacts that are saved on your SIM card memory will not be synced. You would have to copy contacts stored on SIM card to the phone’s memory and then sync with My Contacts App.

See also: "How can I make sure that my contacts are synced automatically?"