Twelve dogs entered a neighbouring enclosure at West Midland Safari Park in the early hours of 9 February as the UK was hit by high winds and heavy rainfall.
Staff were left “extremely saddened” by the loss of six Persian fallow deer and 10 Barbary sheep.
“At no point was there a risk to public safety and there was no danger of any animals escaping the park’s perimeter fencing,” a spokeswoman for the safari park said.
“The wild dogs entered the neighbouring compound through a gated entrance which had been damaged in the storm which hit Worcestershire earlier that morning.
“Given their personal attachment to our animals, our staff are extremely saddened by the incident.”
The spokeswoman said the wild dogs were returned to their compound unharmed.
With Storm Dennis set to bring more bad weather to the UK on Saturday, staff at West Midland Safari Park will be “closely” monitoring the situation to avoid a repeat of last weekend’s incident.
“We are aware of the current weather warnings in place for this weekend and will monitor this closely, making our decisions, as always, in the best interests of our animals and public safety,” the spokeswoman added.
According to the World Wildlife Fund, the African wild dog is one of the world’s most endangered mammals, with only about 1,400 left in the wild.
The largest populations remain in southern Africa and the southern part of east Africa.
The predator, which gathers in packs, hunts species such as gazelles and can run at speeds of more than 44mph.