Northampton Borough Council sold the 4,000-year-old Sekhemka statue in July.
Arts Council England has ruled the council ineligible for a series of grants because of the sale.
The funding was being sought for an exhibition of designer shoes dating from the 19th Century to the present. The council said it was "disappointed".
As well as losing Arts Council "accreditation", the Museums Association has decided to ban the council from membership for five years.
But the authority said it had already decided to resign its membership.
Arts Council England said the sale of Sekhemka breached the accredited standards for how museums managed their collections.
Money from the auction at Christie's was shared with Lord Northampton, whose ancestors donated the statue to Northampton Museum.
The HLF said it had rejected Northampton Council's Collecting Cultures application for £240,400 because it was ineligible for that particular programme.
This programme requires Arts Council eligibility as part of its criteria, a spokeswoman said.
"We would assess any other future applications from the council on their own merits," she said.
The borough council received £130,000 in 2008 from the HLF for a Collecting Cultures project called Trainers, Sneakers, Pumps and Daps.
The council said it understood the HLF had a duty to fund a wide range of projects and was disappointed to miss out.
A council's bid for a Heritage Lottery Fund (HLF) grant of £240,400 has been rejected after it sold an ancient Egyptian statue for nearly £16m.