Firstly, notice that your query variable is called $query1 and your mysql_query is using a variable called $query (variable mismatch?).
You can use mysql_fetch_assoc() to get an associative array from your query.
Using the following code should work, though you should do some checking to make sure that the $result[0] exists.
// Query String
$query1="SELECT needer FROM needer_blood WHERE value_id='$post_id'";
// Run the query
$result=mysql_query($query1) or die(mysql_error());
// Fetch Associative Array
$rows=mysql_fetch_assoc($result);
// Get result [0]: this could result in an error if your query result is empty.
$req_id=$rows[0];
Also, as others have pointed out, mysql is deprecated and you should update to MySQLi or PDO_MySQL if your server supports it. If not, change servers.
Also, as others pointed out, you should watch out for SQL injection. This StackOverflow answer adresses the issue well.