The web player is not designed to be accessed on a mobile device. You should really be using the app; if however you must go to the web player most browsers allow the option to 'Request desktop site'. Try going to play.spotify.com then open the web browsers settings and check this option.
Note: you may need to refresh the webpage after ticking this box.
Please use the search feature before posting a problem/bug/idea. What's a Spotify Rock Star, and how do I become one? Using Spotify Since March 10th 2009 Twitter: @mechanimal82