John Savage, councillor responsible for waste, said residents should leave their glass recycling box at the kerbside if a collection is missed.
This advice came after the Labour councillor was questioned by opposition members at a full council meeting.
Liberal Democrat group leader Richard Blackman asked if glass recycling was still being “effectively deprioritised” due to wider service challenges.
Cllr Savage said the hot weather had seen a rise in sickness absence but said the council was generally coping “pretty well”.
He said: “There has been a few blips.
“I know my own glass collection was missed on one particular Wednesday, which is my collection day, and then I left my crate of glassware out and it was collected on Saturday, so we do mop up collections.
“I am not all that happy with that arrangement. I think it hasn’t been communicated well to the public.
“It is the bottom of the priority list, glassware, because unlike food waste and residual waste and recycling it is the most robust in hot weather and it will not decay and cause a lot of problems like other areas do.
“I’ve stressed with my team where there is a problem, I’ve asked to communicate it better with the public.”
Liberal Democrat Jon Walsh said residents were coming out of their houses to talk to him about missed glass collections, with many saying collections had not taken place on the correct day for months.
Cllr Walsh said: “They have got glass waste that hasn’t been collected and it was a day late, now it is two days late and they were asking me should they just leave their glass waste out indefinitely hoping that it will one day be collected.
“What response should I give to them?”
Cllr Savage said: “My advice would be to leave it there so that it is collected as long as it’s secure on the pavement.
“There are certain areas you wouldn’t want to leave glass out indefinitely, I absolutely agree with that, but it is on that sort of priority list, when we struggle mainly to get drivers because of the absence of a driver, we aren’t going to be leaving people’s food waste or residual waste around.
“It is the glass collections that would normally be deprioritised and I regret that.”
The Labour councillor said the wider waste improvement programme was on track to be delivered over two years.
He said residents could expect to see improvements from the autumn, with new vehicles due to arrive and collection routes being optimised.
Meanwhile, a spokesperson for Hampshire and Isle of Wight Fire and Rescue Service said: “While incidents are relatively uncommon, everyday glass objects can pose a fire risk if left in direct sunlight near combustible materials.
“As a precaution during periods of hot weather, we advise that glass items are not stored in direct sunlight near to anything that could ignite easily.”