The claim was made in a letter from seven consultants in the department to the hospital's medical director.
Patient safety in the Northern Health Trust has been raised on a number of occasions over the last 18 months.
However, it is believed that the recent death of a child has caused further distress among staff.
An investigation is under way into the circumstances surrounding the child's death, which took place after the patient was transferred to the Royal Belfast Hospital for Sick Children.
The child had been brought to the Antrim Area Hospital's A&E department two weeks ago.
The child was transferred to the paediatric intensive care unit in Belfast and placed on a life support machine, but later died.
The case has been reported to the Department of Health and the health board as a "serious adverse incident".
'Hectic'The Northern Trust has confirmed to the BBC that due to staff pressures that evening, it was 20 minutes before the child was triaged or prioritised - that is five minutes more than the trust's own target.
In fact, 21 per cent of people who attended Antrim's emergency department between 17:00 GMT and midnight on Monday 25 March were seen by a triage nurse within the 15-minute target.
Sources have told the BBC that while Monday nights tend to be busy, that particular Monday was "hectic" with nurses having to be taken off general wards and placed in an already overstretched A&E department.
The investigation is examining whether the delay in examining the child affected the child's deteriorating condition.
In a statement, the trust said: "The trust, as a matter of course, carries out a serious adverse incident review in any circumstance involving the trust and its staff, service users or visitors which is 'out of the ordinary'.
"This is best practice and encourages the trust to review procedures and promote a culture of learning."
The statement added that the emergency department at Antrim Area Hospital was built to cater for 30,000 admissions a year but "currently treats upwards of 72,000 patients".
It said a new emergency department was due to open in June with increased capacity.
All seven consultants who work in Antrim's emergency department signed the letter to the medical director.
While their priority is patient safety, it is understood they are frustrated about working in overcrowded conditions and about the lack of nursing staff.
At a Northern Trust board meeting held the same week the child died, a consultant who works in the emergency department asked if the chief executive had been made aware of the incident.
Sean Donaghy said that he was not and asked to be briefed immediately. However, as the child did not die in Antrim Area Hospital, it was not unusual that Mr Donaghy had not been informed.
PerformanceIn the past two years the Northern Health Trust has repeatedly breached waiting time targets.
Most recently, the BBC reported that in the first week of February, 100 patients waited 12 hours or more before being admitted.
There was another major spike from 5 to 11 January when 132 people waited 12 hours or more.
In December, the chairman of the Northern Health Trust, Jim Stewart, was sacked by Health Minister Edwin Poots after targets for the A&E department were not met.
Experts from England were brought in to support the local team in an attempt to boost the unit's performance.
The trust said a range of measures were being introduced to reduce emergency waiting times.
These include introducing an acute medical assessment unit for GPs' direct admission.
Originally set up as a pilot scheme; this is a dedicated area in the hospital for patients referred by their GPs for assessment by hospital consultants.
Previously these patients would have been processed through the emergency department.
The trust is also introducing rapid access medical clinics for GPs to speak to consultants directly or to make a referral.
The report by the experts from Cumbria is expected to be sent to the health minister in May.
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