One of the 11 children described how the trailer went "really fast down the hill" at the farm in Nottinghamshire before it "launched us off".
Two members of teaching staff from Halam Primary and a farmer were also injured in the accident on 11 March.
The acting head teacher of the school has apologised.
One of the children, Ben, said he was frightened and the other children were crying.
"The trailer gone like really fast down the hill and it gone sideways and it launched us off," said Ben.
When asked how it made him feel, Ben said: "It feels like sad."
Ben's mother, Sheree Cockayne, said he has been struggling to sleep since it happened and has been having nightmares and flashbacks.
Mrs Cockayne, who was told about the accident by a school nurse, said: "I rushed to the QMC (Queen's Medical Centre) and Ben was brought in. He had blood all over his face.
"He just laid there really shocked. He had to stay in [hospital] overnight for observation every four hours because he had concussion and felt really sick.
"He's still got bruises to his head, his ribs and his chest, so he still has a few pains."
Nottinghamshire County Council said another child was discharged from hospital after a check-up and one was brought into hospital later in the day for a scan, then released.
A teaching assistant sustained a broken wrist, a teaching student sustained a head wound requiring stitches and the farmer, who was also in the trailer, dislocated his shoulder.
The assistant will be off work for four weeks.
The children were on a trip at Hills Farm in Edingley and the accident happened on Carver's Hollow.
Nottinghamshire Police is investigating the incident, rather then the Health and Safety Executive, because the area where it happened is a highway.
The force has asked anyone with information to contact them.
Hills Farm in Edingley, where it happened, said it would not comment while an investigation is ongoing.
The school's acting head teacher, Paul Nolan, said: "We are very sorry this unfortunate incident happened and we wish the children and adults who were injured a speedy recovery.
"This incident has affected the whole community and everyone is supporting each other as a result."
Marion Clay, the council's acting service director for education standards, said: "This is an established trip for reception pupils and as far as we know at this time all the appropriate procedures were carried out."
A group of primary school children were injured on a trip to a farm when the trailer they were in became detached from the tractor pulling it.