The two, both now 13, admitted the manslaughter of Louise Allen. They had been charged with murder but the prosecution accepted their plea.
Mr Justice Hidden adjourned the case at Nottingham Crown Court for sentencing when evidence will be heard.
Richard Latham, QC, for the prosecution, said a fight started between one of the defendants, who was then 12, and another girl near a fairground in Corby, Northamptonshire, in April. The 12-year-old ended up astride the other girl and at this point Louise Allen, he said, pulled the 12- year-old away. The 13-year-old defendant then intervened.
He said: "It was during the next few seconds, and I use that timing advisedly, something between probably between 30 and 120 seconds, that Louise Allen received injuries to her head which led to her death."
He added: "The evidence of the witness statements suggests that the first defendant [the 13-year-old] kicked Louise Allen to the head and thereafter the second defendant did likewise."
He said: "There is no doubt that the defendants knew that what they were doing was wrong. It is acknowledged by each of them in interview. There is evidence to suggest they had fought before. But that in itself is a long way from proof of the specific intent required for murder. In particular knowledge of the consequence of such a kick in the mind of an adult cannot be assumed in the case of a child." He said the prosecution, having consulted the Crown Prosecution Service and Louise's parents, had decided it would be improper to pursue a murder charge.
Sally Bennett-Jenkins, representing the 13-year-old, said her client went to the help of her friend who was involved in a fight "who she perceived was being outnumbered two to one by both the other girl and the intervention of Louise Allen".