This is business, and when it comes to how much you're worth you should never feel bad about asserting your worth. However...
"to avoid wasting both of us time, this is the maximum salary we can give you"
This is interesting. It could be one of two things: this is either a strategy to keep your from being aggressive or assertive about what you deserve OR the truth. If it's the truth, you can still push back, ONCE. I would say "Are you saying that is non-negotiable?", if they respond "Yes, it's non-negotiable." Then I would make my decision.
However if it's just a strategy to keep you from negotiating what you want, then they'll bend a bit.
But the overall response here is: You should never be ashamed of asserting your worth. In business and in life. People will want you to compromise constantly. You can, if you want, but you should never feel embarrassed or ashamed asserting your worth. It's not disrespectful, it's business.
Do you think the company is embarrassed when it charges clients its fee? No, it isn't. That's business. They do their business and you do yours.