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, or council employee Paul Livingstone had received relevant training about reversing.
Glasgow City Council pled guilty at Glasgow Sheriff Court to flouting health and safety legislation by failing to ensure all employees using the refuse collection vehicles had received adequate training.
As a result Mr Kerr drove without the aid of a reversing assistant, hit Mr Malcolm and reversed over him.
The court was told that between March and December 2011 the council provided reversing assistant training to its refuse collection drivers. Staff were told that if reversing cannot be avoided to use assistants, and gave advice about where an assistant should stand, and how to indicate to the driver when it is safe.
Procurator fiscal depute Louise Beattie told the court: "Mr Kerr had been assessed as to driver safety but his training had not encompassed reversing maneouvres."
Defence counsel Emma Toner said that changes had since been put in place by the council.
Sheriff Sam Cathcart deferred sentence until next month.