It seems impossible. You must remove AutoPostBack="true" and try another way to perform postback. Consider below solution:
when dropdown ddlCountry changed, the function ddlCountry_changed is called that trigger btnLoad click to perform postback. The button btnLoad is put inside an update panel so the page is not reload and you still have focus on the dropdown.
<script type="text/javascript">
function ddlCountry_changed() {
document.getElementById('<%= btnLoad.ClientID %>').click();
}
</script>
Country:
<asp:DropDownList ID="ddlCountry" runat="server" onchange="ddlCountry_changed();">
<asp:ListItem Text="Vietnam" Value="1"></asp:ListItem>
<asp:ListItem Text="United State" Value="2"></asp:ListItem>
</asp:DropDownList>
<asp:UpdatePanel ID="updatePanel" runat="server">
<ContentTemplate>
<asp:Button ID="btnLoad" style="display: none" runat="server" OnClick="btnLoad_OnClick" />
</ContentTemplate>
</asp:UpdatePanel>