The breach of hunt rules was announced just days before MPs voted for a total ban on hunting with dogs.
Hunt spokesman Michael Clayton said: "The masters knew nothing about it whatsoever, but they accept somebody's got to carry the can.
"We regret very much that this has happened."
All four masters – including Scalford businessman David Manning – were suspended after an animal welfare group released incriminating camera footage on Friday.
Huntsman Neil Coleman and employee Dean Jones were also suspended.
Investigators from the International Fund for Animal Welfare have been monitoring the hunt's activity for two years.
In March they caught Mr Jones moving a vixen and two tiny cubs to an artificial earth – made of brick and plastic piping – using a hidden camera.
Mr Clayton said: "He meant well. He was moving them from somewhere they were definitely at risk. They were on a sheep farm – somebody was going to bump them off."
But IFAW worker Lis Key says the camera footage shows the artificial earth was also in the middle of a sheep field.
She added: "This goes against the argument that foxes are a pest which hunts are helping to control.
"It shows they are actively encouraging them on to hunt land."
The IFAW says camera footage shows Mr Jones putting two-week-old cubs into a brick chamber and covering it with a concrete slab, earth and leaves.
"The exits were also blocked, with bricks and earth," added Mrs Key, who says the foxes were left trapped for nine days.
The masters – Mr Manning, bloodstock agent Charles Gordon-Watson and farmers Nicholas Wright and Roger Dungworth – were to appear before the Masters of Foxhounds Association yesterday.
Mr Jones and his boss Mr Coleman could lose their jobs if they are proved to have broken hunt rules. And the masters could face further suspensions or a fine.
Mr Clayton says IFAW withheld the footage until just before the Commons debate on Tuesday to boost anti-hunt feeling.
But Mrs Key says it took months for the film to be edited and checked by lawyers.
l Melton MP Alan Duncan was in Jerusalem on Tuesday and did not vote in the Commons' debate.
But yesterday he said: "When our transport system, schools and hospitals are in crisis, the Labour Party's obsession with this one issue shows it is out of touch with the priorities of the country at large.
"I believe this vote will be the cause of deep and lasting resentment by country people who see their way of life increasingly under threat."
alice.ryan@meltontimes.co.uk