He had been working in the Grimsby area at the time with some of his family, who are roofers.
The cause of his death remains a mystery, with Gary's family saying police could have done more to find out what happened.
"Obviously as a family we are devastated," said Gary's nephew, Jamie. "We need closure. We need answers."
Gary, who lived in Miles Hill in Leeds, had been out watching the game with family and colleagues before heading back to their lodgings.
The alarm was not raised as Gary left for a walk, as this is something he often did to clear his head.
His body was found around one hour and 20 minutes' walk away from where he was staying.
"How can a guy go missing for more than 24 hours and nobody see him, then end up on a beach?" said Jamie, 37.
Only one CCTV camera caught Gary, close to where he was staying.
Jamie said the family had been told by police that other CCTV cameras in the area that might have picked him up were either dummies, broken, or had been rewritten after 24 hours.
The family is frustrated at what they feel was time wasted questioning colleagues and family about his disappearance - time they feel would have been better spent gathering CCTV early on.
"He's just disappeared out of our life," said Jamie. "We are going to be grieving until we get some sort of closure."
To make matters worse, the authorities kept Gary's body for three months after he died while they carried out investigations.
By the time the family got Gary back, the extent of the damage to his body from the autopsy meant they were advised not to see him before the funeral.
"We never got to say goodbye to him," Jamie added.
Gary's funeral was held in June and the wake was held in the Eddie Gray suite at Elland Road.
Detective Constable Nichola Oakley, from Humberside Police’s Major Crime Team, said: “We have been working very closely with Mr Simpson’s family following his sad death in May in Cleethorpes.
“We know Mr Simpson was last seen at his rented accommodation on Strathmore Court in New Waltham around midnight on Wednesday 15 May, and may have left that address around 6am on the Thursday.
“Officers have trawled through hours and hours of CCTV footage to try and ascertain where Mr Simpson went following that time.
“We have appealed over the last few months to the public to come forward, who could offer help with our enquiries, and we have followed up numerous lines of enquiry.
“We are not treating Mr Simpson’s death as suspicious. There will be an official coroner’s hearing in due course.
“If anyone can assist in helping us piece together Mr Simpson’s last few hours please do contact us quoting log 111 of 17/05/19.”