When you really start to dig into the nuances of a salary negotiation, it will become apparent that salary is only one component of what's on the table for discussion.
Don't forget about...
Flex work schedule
Professional development funding
Contribution toward health insurance premiums
Student loan payment contributions
When negotiating, it's important to specifically ask where there is flexibility in the offer, as well as what your overall priorities are in the negotiation process.
Approaching a negotiation from a position of gratitude and inquiry can help you find success in your negotiation. In this example, even if the salary did not have room to be raised, the door is open for the employer to offer something else in lieu of higher take home pay.