How can I get response of Confirm popup in C# code?

One idea can be to put a hidden field in the form and set the value on user responding to the confirm box.
Lets say, the hidden field is -

<asp:hiddenfield id="hdnConf" runat="server" xmlns:asp="#unknown" />

Now, let's modify your code accordingly.

Page.ClientScript.RegisterStartupScript(Page.GetType(), "Message Box", "<script language="'javascript'">if (confirm('This is confirm popup')) document.getElementById('<%=hdnConf.ClientID%>').value='true'; else document.getElementById('<%=hdnConf.ClientID%>').value='false';</script>");

//get confirmation value
bool confResult=bool.Parse(hdnConf.Value.ToString());

This is purely untested code and hence you may need to modify a little.

Hope, it helps :)