The authority has chosen the Highbury estate in Cosham to trial wheelie bins for general household rubbish.
It is part of a bid to cut down the amount of waste collected and to promote recycling.
Residents were told to stop putting out bin bags because a black wheelie bin would be provided for sacks of non-recyclable waste.
But those living in the area say the new bins – smaller than a standard recycling one issued by the council – aren’t big enough and rubbish collectors refused to collect extra waste over Christmas.
Highbury resident Glenn Nichols, 54, said: ‘It’s a brilliant idea – but when the council first introduced the bins I thought; “is that the size of it?”.
‘For the three of us living at home, it’s a struggle.
‘The issue was at Christmas. It’s a time when we all accumulate more waste and we thought the bin men would give us some leeway. But they didn’t.
‘The whole street had bins everywhere.’
Sarah Turner, 34, says she was told to store her eight sacks of extra rubbish – or take them to the tip.
She said: ‘Why should I have to take my rubbish to the tip when I pay council tax like the rest of Portsmouth, who get their extra rubbish taken away? If the bins were the same size as a normal wheelie bin, it wouldn’t be as bad.’
Another annoyed resident said: ‘Some of the wheelie bins they opened, if they had a single bag in they pulled them out and threw them on to the truck otherwise they used the wheelie bins.
‘When they got to ours one man collected the wheelie bin, pointed at the extra bags and spoke with a colleague, returned our wheelie bin then walked on to the next house leaving said bags behind.
‘Considering that they were willing to take out a single bag from a wheelie bin, rather than use the wheelie bin, I’m a little annoyed.
‘It can’t be the case of “we may cause injury on picking up the bags” seeing as they were stretching to the bottom of a wheelie bin to pull out a bin bag, which would be incorrectly lifting a possibly heavy bag in any case.
‘I’m now left with an already full wheelie bin ready for next week’s collection.’
The six-month trial began in September.
The council says it hasn’t promoted the trial city-wide as the changes are only limited to a small area.
Colette Hill, the council’s assistant director of property and housing, said: ‘We appreciate residents’ co-operation with the trial, the Christmas period is always going to generate more rubbish and recycling and this was the first Christmas we’ve used wheelie bins so we were lenient with the ‘closed lid’ policy during the festive period.
‘We’ll be reviewing the trial period as a whole before we make any decisions about future waste collection and will take on board feedback from residents.
‘It’s our commitment to reduce the amount of rubbish we collect, improve the cleanliness of the streets and encourage people to recycle more – and residents have fed back that they feel that the streets are cleaner.’
The homes in the following roads are included in the trial; Windsor Road, Hawthorn Crescent, Chatsworth Avenue, Highbury Way, Highbury Grove, Dovercourt Road, The Old Road, Donaldson Road, Tudor Crescent, Old College Walk, Elgin Road, Pitreavie Road, Edgerly Gardens and Jasmond Road.
The trial also includes all homes from 1 to 75 Portsmouth Road (including Highbury Buildings).