Great grandfather Malcolm McCulloch, 71, was hit by the reversing vehicle and dragged along the ground and later died from chest and pelvic injuries.
Risk assessments in place at the time by the council record that "reversing assistant training was to be completed by all refuse collectors by August 2011".
But on August 10, 2012, a year after the deadline, neither agency worker Shaun Kerr, who was driving the vehicle, nor council employee Paul Livingstone had received relevant training.
Glasgow City Council pled guilty at Glasgow Sheriff Court to flouting health and safety legislation by failing to ensure all employees using refuse collection vehicles had adequate training.
As a result Mr Kerr drove without the aid of a reversing assistant, hit Mr Malcolm, reversed over him and dragged him, which caused him to die of his injuries.
The court heard that between March and December 2011 the council provided reversing assistant training to refuse collection drivers.
During the training, staff were told that if reversing cannot be avoided to use assistants, and gave advice about where an assistant should stand, how they should check it's safe to move and how to indicate to the driver when it is safe.
Procurator fiscal depute Louise Beattie told the court: "Mr Kerr had not undertaken reversing assistant training.
"He had been assessed as to driver safety but his training had not encompassed reversing maneouvres."
The court was told agency drivers did not get reversing assistant training and that Mr Livingstone, a council employee for 21 years, had not received it either.
Defence counsel Emma Toner said changes had since been put in place by the council and all employees, including agency workers, are trained and records of training kept up to date.
Sheriff Sam Cathcart deferred sentence until next month.