The University Hospitals Coventry & Warwickshire (UHCW) NHS Trust had more stillbirths and neonatal deaths per 1,000 births compared to similar services in 2020.
The Trust's rate for each incident and the two combined was 5% higher than average for the UK's 28 Neonatal Intensive Care Units.
The research was carried out by the Mothers and Babies: Reducing Risk through Audit and Confidential Enquiries (MBRRACE) group and released in a report last month.
Stillbirths happen when a baby is lost at or after 24 weeks pregnancy, and neonatal deaths happen when a baby dies within the first 28 days of its life.
Only 5 other NHS Trusts in the UK received the worst rating of 'red' for their perinatal mortality rates in the MBRRACE report.
A spokesperson for UHCW told the Local Democracy Reporting Service (LDRS) it had seen a rise in women not knowing they were pregnant and fetal anomalies during the pandemic.
They said: "As a Level 3 tertiary unit we receive referrals from all over the county for women, often with complex medical backgrounds, who require intensive and emergency care.
"We have been supporting an increase in requests from other maternity units to care for complex conditions including suspected fetal anomalies, enhanced maternal medicine needs and suspected pre-term births.
"During the pandemic in 2020, which is the period that this data relates to, we saw a rise in patients with diagnosed fetal anomalies and women who did not know that they were pregnant and were therefore not booked for antenatal care.
The spokesperson added that the Trust has been "working closely" with GPs and external agencies to support women who report unusual abdominal discomfort or amenorrhea (absence of periods) as a priority. They added that "this will help to identify women who may be pregnant".
UHCW manages University Hospital Coventry and the Hospital of St Cross in Rugby.
2020 is the first year that the Trust received a 'red' for its record on pre and post-birth baby deaths.
There were 5,564 births at the Trust this year, continuing a steady decline since the over 6,000 recorded in 2017.
Rates of stillbirth and neonatal death in 2020 were given as 'crude' and 'adjusted' figures, each showing a different picture.
UHCW's crude rate for perinatal deaths was 7.37 per 1,000 births, down to 6.65 when not including congenital abnormalities.
This is higher than the overall rate the report gave for the UK, of 4.85 stillbirths and neonatal deaths per thousand births.
But the adjusted rates at the Trust came in at 5.94 and 5.03 respectively - much closer to the national average.
"We aim to provide a safe, high quality, personalised experience for patients and their families throughout pregnancy, birth and the postnatal period," the spokesperson for UHCW added.
"Patients and their families are always at the forefront of our focus and we are continuously listening and learning from their experiences to ensure the best possible outcomes."