He described the piling up of rubbish over the festive period as "disappointing" as it emerged households had gone for up to four weeks without their bins being emptied.
Officials at one local authority suggested that householders should seek out purchases which had the least packaging to minimise the problem.
The situation this year was made particularly bad because of the heavy snow which preceded Christmas over much of the country, which led to many local authorities cancelling collectiion services on health and safety grounds directly ahead of the period when services were further reduced because of a series of three bank holidays.
Mr Neill said: "We need to think again about how we maintain these basic services over the holiday period.
"People do produce a lot of rubbish over Christmas, and it is disappointing that in some cases councils haven't shown more initiative about how to ensure people still get the services they pay for."
The problem has been exacerbated by householders failing to realise that their collection days have been changed and so missing them.
Birmingham was said to be especially troubled by delays to bin collections because of a strike before Christmas.
Kevin Mitchell, Birmingham city council's assistant director of fleet and waste management, said: "It is a triple whammy.
"This all happened during Christmas, with three Bank Holidays and 420,000 extra turkey carcasses to collect."
Haringey council in north London has suggested people should "buy items with minimal packaging to reduce waste".
In Leeds, where bin collection routes were changed in October, the service has been chaotic, with missed collections for thousands. Some claimed green bins had not be emptied for three months.