The edit really fooled a lot of people, including me!
'\' is a special character in regular expressions - it effectively is an escape character or denotes an escape sequence.
So the RegEx engine sees DebugLogs*\C*onfigurationServices.log which is, indeed, an unrecognized escape sequence. \A actually is an existing escape sequence.
So you need to escape the escape character. The simplest way to do this is to double the number of slashes used:
Regex.IsMatch("\\\\Application.evtx", "DebugLogs\\\\ConfigurationServices.log");
Which the RegEx engine will see as comparisons betweeen "\\Appplication.evtx" and "DebugLogs\\ConfigurationServices.log" - now the backslash has been escaped and has no special meaning.
Regex.IsMatch(@"\\Application.evtx", @"DebugLogs\\ConfigurationServices.log");
works fine too and is more readable.