MVVM is a client-side feature which is not related to the server technology that you are using - you are free to use is with whatever technology you like e.g. PHP, JSP, NodeJS, ASP.NET WebForms/ MVC etc.
Since you did not share any details about your setup It is not getting clear what exactly causes your setup not to work. Anyway we are not aware of any issues caused by the using of ASP.NET Webforms.
Join us on our journey to create the world's most complete HTML 5 UI Framework - download Kendo UI