I faced similar problem to perform login operation of a web page.
Used below piece of code and it worked for me.
 

using System;
using System.Collections;
using System.ComponentModel;
using System.Data;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Windows.Forms;
using System.Xml;
using System.Runtime.InteropServices;
using System.Windows;

namespace Dynamic.Script_8D764454627C233
{
	// Script generated by Pega Robotics Studio 8.0.2012.0
	// Please use caution when modifying class name, namespace or attributes
	[OpenSpan.TypeManagement.DynamicTypeAttribute()]
	[OpenSpan.Design.ComponentIdentityAttribute("Script-8D764454627C233")]
	public sealed class Script
	{ [DllImportAttribute("User32.dll")]
	   public static extern IntPtr FindWindow(String ClassName, String WindowName);
	  [DllImportAttribute("User32.dll")]
	  public  static extern IntPtr SetForegroundWindow(IntPtr hWnd);
	  [DllImport("user32.dll", CharSet = CharSet.Auto, SetLastError = true)]
	  public static extern  IntPtr SendMessage(IntPtr hwnd, uint Msg, IntPtr wParam, IntPtr lParam);
	  [DllImport("user32.dll", CharSet = CharSet.Auto, SetLastError = true)]
	  public static extern IntPtr FindWindowEx(IntPtr hwndParent, IntPtr hwndChildAfter, string lpszClass, string lpszWindow);
		
public void LoginWindow(string Uname,string Password)
        {
 	 try
	 {  
	 System.Threading.Thread.Sleep(2000);
	 IntPtr hWnd = FindWindow(null, "Windows Security");
    // Windows Security is the title of the alert box 
	 SetForegroundWindow(hWnd);
	 System.Threading.Thread.Sleep(2000);

	 SendKeys.SendWait(Uname);
	 System.Threading.Thread.Sleep(1000);
	  SendKeys.SendWait("{Tab}");

	  SendKeys.SendWait(Password);
	  System.Threading.Thread.Sleep(1000);

	  SendKeys.SendWait(@"{Enter}");
	  }
  catch(Exception ex)
	{
    OpenSpan.Diagnostics.Diagnostic.PublishException(ex, null); 
  	}

}
}

In your case sending the Enter key  alone will solve your problem.