You realize that when you told them what you wanted in terms of salary they expected that it would be enough. You are now in a difficult spot because you now want more. If you are going to ask for more they will want to know why? You might be able to convince them that their benefits aren't as good as you expected, or the commute will be more expensive, but they don't have to change their offer.
Imagine the following scenario. The jobs with that title pay 40K to 50K. They asked how much you wanted you said 45K. They were pleased to hear that number. It is in the middle of the range, it saves them some money, and gives them room to give you a raise next year. Therefore your application moves to the next round of the hiring process. Now you tell them the truth, you want 55K. There is now an issue. They can't meet your request, it is more than they can pay somebody in that position. But even if they offered you the top of the scale (50K) they don't have room to give you a raise next year. Employees never want to be at the top of the scale, it reduces the chances of a raise. Employers don't want employees at the top of scale, because they aren't motivated.
They now worry that they have wasted their time regarding your application and offer, you were never a serious candidate. They also worry that even if you accept either the current offer, or their improved offer, you will be unhappy, and not be with the company for very long.
It comes down to how much are you willing to risk. You can accept the current offer, and don't plan on staying for very long. Or you can try and ask for a better deal, and realize they now are concerned about you. You might or might not get it. Or they can reject your bid for a better deal and never hire you.
If the question describes the situation accurately, you aren't being greedy. You just did a poor job of answering their question.