The premises in Mundles Lane, behind St George’s Church in East Boldon, were targeted overnight on Tuesday.
Up to 20 locks have been smashed by yobs while two goats and six ducks were taken, as well as hens.
The goats, named Lottie and Gypsy, which were both nabbed in the theft belonged to pensioner Fred Rylands and he says he will no longer keep up with the allotment.
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“I just can’t believe it,” said an emotional Mr Rylands, 72, who is a retired milkman.
“They’ve broken almost every single lock and taken the goats which were my pride and joy.
“My family has been here for 150 years and for this to happen is just devastating.
“The goats are tagged so I hope that they can be traced and I can get them back.
“I’ve had things stolen before but nothing as bad as this.”
Mr Ryland discovered the damage on Wednesday morning after he had visited his plot the evening before.
Police have confirmed that they are investigating the incident in a bid to track down those responsible.
Despite keeping animals and developing his allotment site for decades, Mr Rylands says this latest setback has deterred him keeping it in future.
“Because of what’s happened, I’m going to call it a day,” he added.
“This has really put me off and I can’t take it anymore.
“It’s only a hobby to me but to lose the goats like this is really upsetting.
“It would cost about £300 of £400 to replace them, but I can’t put a price on what they meant to me.
“I’ve had things stolen before and they’ve turned up again so maybe there’s a chance I’ll get them back.
“The locks alone were £15 each too.”
A spokeswoman for Northumbria Police said of the incident: “Police are appealing for information following a break-in at allotments in East Boldon.
“A number of allotment plots were targeted in an incident on Mundles Lane, which took place between Tuesday evening and Wednesday morning.
“Locks were reported to have been broken, and much-loved livestock has been stolen.
“Officers are asking anyone who may have seen anything or has information that could help their enquiry to contact them on 101 quoting log 1263 130617.”