Just have a MAC is not enough. To be able to support web configuration, you need to run an embedded webserver, such as Apache (embedded version). So you need to have a CPU that runs the embedded OS, with TCP/IP.
The good news is that you have a lot of choice these days to implement this. One popular solution is to run embedded linux on ARM, with Apache (and Tomcat perhaps if you need Application Server). The MAC will be just a peripheral that beneath the TCP/IP.