The issue was highlighted as part of a day of coverage across the BBC in England, which is taking a closer look at what happens to the rubbish we all create.
According to government figures, recycling rates across the Westmorland and Furness area are at 53% – above the England average of 42%.
“In terms of what you put out on your doorstep, in terms of the recycling materials, most of that is fully recycled,” Jones told BBC Radio Cumbria.
“There is some small amount of wastage because of contamination.”
However, the area has the eighth highest amount of household waste thrown away per person.
The most recent figures available show people living in the local authority area threw away 460.2kg in a year. The highest figure was 592.8kg in the Isles of Scilly.
The council said people putting recycling materials into non-recycling waste was to blame.
Jones said the authority spent £30m a year in dealing with bin collections.
She added non-recyclable household waste was diverted away from landfill and made into fuel.
“We do pretty well here in Cumbria for recycling,” she added.