The 13 caravans and associated vehicles arrived on Sunday evening setting up camp near to the main entrance, in a field close to the perimeter wall.
Park officials have since unlocked two metal padlocked gates to prevent further damage to the park.
The gates at the park are ornamental and do not close, resulting 24-hour access.
Northamptonshire Police officers visited the park this afternoon (Tuesday, June 18) to speak to staff.
David Ball, organiser of Corby Conspiracy Morris Dancers who meet weekly in the park, said: “It’s not going to be a problem, as long as they don’t create any mess or do any damage.”
Mother of two Aliina Atkinson, from Desborough, said: “I can’t see them staying for long.
“I’m not going to have a go at them - there aren’t any signs up about not camping.
“If they don’t pick up their rubbish then that wouldn’t be good but people need to be a bit more reasonable to other human beings that live their lives differently.”
Residents of East Carlton village have been feeling ‘uneasy’ since the Travellers moved in.
One resident who did not wish to be named said: “I’ve had to lock my doors - I feel uneasy.
“They have had their generators running 24-7.
“Simply they should not be there and they will leave a mess.”
It is understood that the Travellers had been staying in Weldon Woodland Country Park in Kettering Road, another Corby Council-owned green space.
John Underwood, chairman of East Carlton Parish Council, said: “It is disappointing that it has been so easy for this to happen.
“The parish council would like Corby Council to invest in better gates, perhaps electric ones that allow residents of East Carlton Hall to gain access and for the park to be closed from dusk until dawn.
“Investing in a barrier system would prevent vandalism and other anti-social activities which sometimes take place including drug abuse and car nuisance.
“The team at the park are constantly maintaining the park and they do an excellent job but we need investment to ensure the travellers don’t use the park again.”
Cllr Underwood, who is also a member of The Friends of East Carlton Park group, added: “It’s getting harder and harder for Travellers to find places to stay with the measures being taken to stop them using their usual stops.
“There should be more official places for them to use.”
A spokesman for Northamptonshire County Council said: “Assessments are being carried out today with a view to seeing what action can be taken.”
Corby Council has been contacted for a comment.