See i have also used the Update Panel but i am able to change the Textbox value. here is my code.
Make sure the TextBox is inside UpdatePanel
HTML: 
<form id="form1" runat="server">
    <div>
        <asp:ScriptManager runat="server">
        </asp:ScriptManager>
        <asp:UpdatePanel ID="upUpdatePanel" runat="server">
            <ContentTemplate>
                <asp:DropDownList ID="ddlDropDownDemo" AutoPostBack="True" OnSelectedIndexChanged="DropdownlistChanged"
                    runat="server">
                </asp:DropDownList>
                <asp:TextBox ID="txtDemo1" runat="server" />
            </ContentTemplate>
        </asp:UpdatePanel>
    </div>
    </form>
C#:
protected void Page_Load(object sender, EventArgs e)
        {
            if (!this.IsPostBack)
            {
                this.BindDropDownList();
            }
        }
        private void BindDropDownList()
        {
            string constr = ConfigurationManager.ConnectionStrings["ConString"].ConnectionString;
            using (SqlConnection _cn = new SqlConnection(constr))
            {
                using (SqlCommand _cmd = new SqlCommand("SelectName", _cn))
                {                    
                    _cmd.CommandType = CommandType.StoredProcedure;
                    _cn.Open();
                    using (SqlDataReader _dr = _cmd.ExecuteReader())
                    {
                        if (_dr.HasRows)
                        {
                            ddlDropDownDemo.DataSource = _dr;
                            ddlDropDownDemo.DataTextField = "LastName";
                            ddlDropDownDemo.DataValueField = "EmployeeID";
                            ddlDropDownDemo.DataBind();
                        }
                    }
                    _cn.Close();
                }
            }
        }
        protected void DropdownlistChanged(object sender, EventArgs e)
        {
            txtDemo1.Text = "correct";
        }
Thanks & Regards,
Azimuddin.