When you are sending an e-mail through a server that requires SMTP Auth, you really need to specify it, and set the host, username and password (and maybe the port if it is not the default one - 25).
For example, I usually use PHPMailer with similar settings to this ones:
$mail = new PHPMailer();
// Settings
$mail->IsSMTP();
$mail->CharSet = 'UTF-8';
$mail->Host = "mail.example.com"; // SMTP server example
$mail->SMTPDebug = 0; // enables SMTP debug information (for testing)
$mail->SMTPAuth = true; // enable SMTP authentication
$mail->Port = 25; // set the SMTP port for the GMAIL server
$mail->Username = "username"; // SMTP account username example
$mail->Password = "password"; // SMTP account password example
// Content
$mail->isHTML(true); // Set email format to HTML
$mail->Subject = 'Here is the subject';
$mail->Body = 'This is the HTML message body <b>in bold!</b>';
$mail->AltBody = 'This is the body in plain text for non-HTML mail clients';
$mail->send();
You can find more about PHPMailer here: https://github.com/PHPMailer/PHPMailer