Hereford's owner Arena Racing Company claimed it was still open to negotiation over the potential for the racecourse to be re-opened at some stage in the future.
Only 17 years remain on the lease for the National Hunt venue with Herefordshire Council, and with ARC maintaining it is not financially viable to keep it open, the track on Sunday became the first in Britain to close since Stockton in 1981.
ARC is to close a second course, Folkestone, on Tuesday.
Assistant racing director (south) Jim Allen said: "It closes today but we're leaving two groundstaff here and keeping everything as it is as a racecourse.
"The fences and running rail will be maintained as well, we will be cutting and fertilising the track and there will be a site manager to maintain stands and buildings.
"We're still willing to talk to anyone that comes along but at the moment no-one has approached us.
"We'd like to see racing continue at Hereford at some point in the future and we'll do what we can to make that happen. The same goes at Folkestone."
Allen went on: "There has been one redundancy and all the rest of the staff have found new jobs."
Racing was first staged at Hereford in 1771 and the track is within the city, meaning it would have considerable potential for development in the future.
It has been commented that ARC has been running the course down in preparation for its demise, but Allen did offer a chink of light over the possibility of the council offering a new lease.
"There are 17 years left on the lease and any racecourse or body can come and talk to us about it," he said.
"The council has come back to us about a new 125-year lease, but this has only recently been received. It is very brief and there will be a meeting at some point in the new year.
"We'll be maintaining it, it will stay as it and there is still every opportunity that some fixtures in 2014 will return here.
"The BHA normally start the fixture list around February and finish in June or July and we've applied for a licence for Hereford next year."
However, Allen said: "We are preparing to shut down and are not expecting to race in 2013.
"In 2014 I could see it in action, but the nuts and bolts of it are it doesn't make much money and that's why we're closing it.
"Two years ago it staged 19 meetings, still not making money and even with media rights having improved, it was still not financially viable.
"They are big beasts to run, and no business people have come to us to take it on."