The missile did not detonate but caused a fire which killed 20 sailors.
Veterans from HMS Sheffield’s ship’s company and their families gather every year at the Falklands Memorial in Broad Street, Old Portsmouth, to mark the loss.
For yesterday’s service they were also joined by sailors from HMS Arrow and HMS Yarmouth who were involved in rescuing survivors.
HMS Arrow saved 260 sailors.
Chris Purcell was on board when the missile hit the ship in 1982.
The 59-year-old said: ‘I was in the galley 10 minutes before it happened and everyone I had just been talking to was killed. I will always remember them and this service is extremely emotional. It means a lot that so many people are here.’
Wife Louise said: ‘I feel like I was there the number of times he has told me what happened. I know those memories will never leave his head and he does suffer.
‘Luckily we have a doctor who is brilliant. Civilians and health professionals will never fully understand PTSD and there is no cure, but we have to make sure there is somewhere for them to go and talk and someone to listen.’
The Lord Mayor of Portsmouth, Councillor Lee Mason, attended to lay a wreath and a band led a procession.
Commander Mike Norman was First Lieutenant on board HMS Sheffield and also went along to the memorial event.
He said: ‘It is very moving to be here and it is so nice to see our former shipmates again.
‘We are now 37 years from what happened but those memories are as bright to me as when they first happened.
‘We lost 20 people that day and we must continue to remember them.’