Barrow Council was considering David Gill's fitness to hold a licence after his conviction in November for allowing potentially invasive sacred ibis to fly out of South Lakes Wild Animal Park.
It concluded that the offences were inadequate to justify closing the zoo.
However, councillors could refer back to the warning if they have to consider his suitability on another occasion.
Mr Gill, who has not commented, was convicted of three offences under the Wildlife and Countryside Act and fined Â£2,000 in November.
The birds, which are native to Africa, are on a list of species the authorities do not want settled in the UK as they can cause significant damage to other species.
Barrow Council's licensing regulatory committee said that Mr Gill had given assurances that procedures were now in place to prevent any future escape occurring.
The council has still has to decide whether to bring any health and safety prosecution over the death of keeper Sarah McClay, who was mauled by a tiger at the same venue in May 2013.
She suffered puncture wounds to her head and neck when the animal got through an open door to a corridor she was working in.
The owner of an animal park in Cumbria has been served with a warning over the escape of a "threatening" bird.