As @1muflon1 said in his answer, the term real income is used in economics to denote your income after adjusting for inflation and is only useful if you compare incomes over time. That's probably not what you are talking about.
Since you already deducted taxes (and maybe social security charges) from your gross income, in economics terms your salary of \$900 is your net income or disposable income. If you subtract payments for necessities like housing, clothing, food, and gasoline, then what is left over, \$730 in your case, is called your discretionary income. That's basically what you can spend or save after having subtracted all expenses necessary to survive and keep your job.
Since what you earn usually means your net income, your father is right in saying that you "earn a lot", given that you admit that your salary is a "large" salary. "Large" can of course be understood only in relative terms, so I guess you mean that your net income is considerably above some average or median in your country.
However, the costs of necessities should not differ too much between individuals except under special circumstances like if you live with your parents and therefore have no expenses for housing (since you didn't mention these expenses). This would imply that if your net income is "large", then also your discretionary income should be "large". (And in case you have no housing expenses this should be even more true.) Thus, it's not clear why you say "it is not so", referring to your calculation of your discretionary income.
In case you are comparing your discretionary income with your country's average net income, this would simply be a meaningless comparison. You should of course compare it to your country's average discretionary income.
So given the explicit and implicit information in your question I'd say your father is right.