Paul Knight, 40, of Bexhill Road, St Leonards, died outside the store in John Macadam Way, off Sedlescombe Road North, on July 2.
Three men, aged 28, 24 and 53, who were arrested on suspicion of manslaughter have now been released under investigation, police said.
Police were called to the Sainsbury’s store after reports of a shoplifting offence at 9.45pm on Tuesday (July 2).
Despite attempts by police and paramedics to resuscitate the man, he was pronounced dead at the scene.
Detective Chief Inspector Alex Geldart from the Surrey and Sussex Major Crime Team said: “This is a tragic incident and our thoughts are with the man’s family and friends at this time.
“We would like to hear from anyone who was in the store or just outside the entrance on Tuesday evening at about 9.30pm who may have witnessed something which could help with our investigation.”
Anyone who witnessed the incident or who may have relevant mobile phone footage, is asked to contact police online (https://www.sussex.police.uk/contact/af/contact-us/) or by phoning 101, quoting Operation Millbank.
Police said the Independent Office for Police Conduct (IOPC) is carrying out an independent investigation into the death after a mandatory referral was made by Sussex Police Professional Standards Department due to the attendance of police to the incident.
Shortly after the death, a Sainsbury’s spokesman said: “We are helping the police with their enquiries. Our thoughts are with the person’s family.”