The servicemen, from Bicester-based 206 Squadron, were in an armoured vehicle on patrol in northern Helmand.
Capt Gordon Fletcher, Staff Sgt Paul Bingham, L/Cpl Daniel Rushton and Craftsman Jamie Bewick were able to drive away after hitting the device.
On Wednesday it was announced a British soldier had been killed in an explosion on patrol in southern Afghanistan.
Capt Fletcher, of the Royal Logistic Corps, was the vehicle commander.
'State of shock'
He said: "After the initial shock of the explosion and the dust cloud in the vehicle had subsided our first reaction was one of disorientation.
"[We were] trying to take in the severity of the event that had just happened, followed by what felt like minutes but most probably seconds of almost silence.
"Due to the size of the explosion we were unsure of the extent of the damage to the vehicle. On further examination the vehicle was able to drive on its own accord out of the contact area.
"Part of the vehicle training and safety brief covers the wearing of both seat belts and helmets which ultimately saved the crew from sustaining any major injuries during the blast."
Craftsman Bewick, of the Royal Electrical and Mechanical Engineers, was driving the vehicle.
He said: "At first you are in a state of shock but then your training kicks in and the priority is the crew, ensuring everybody is uninjured and safe."
The troops were part of a re-supply convoy of essential equipment when their vehicle was hit last month.
A total of 166 British service personnel have been killed on operations in Afghanistan since 2001.