The English singer-songwriter is set to return to New Zealand as part of his "Loop Tour" early next year.
He will make three stops — in Auckland, Wellington and Christchurch — between January 16 and 24, before heading to Australia for eight shows.
Mr Radich said it was a struggle to get acts to Dunedin because "we’re not an international airport".
"Any act we get will land in Christchurch first."
Dunedin was not going to turn into a "wide-body jet airport" any time soon, so it was difficult for international acts to have their equipment transported to the city.
Dunedin Airport resumed international flights from Australia in June this year when it received a Jetstar flight from Gold Coast Airport.
Mr Radich said Sheeran might have decided to go to other venues to give other people around New Zealand a chance to attend his concerts.
Dunedin Venues chief executive Paul Doorn said it was a "bit of a shame" Sheeran was not coming to the city.
"A bit disappointed from my perspective ... we’d like to think that we were always an option."
Sheeran’s three sold-out shows in 2018 at Forsyth Barr Stadium were hugely successful for Dunedin.
