Leon Elcock, 16, and Hamza Lyzai, 15, were detained for four and a half years and three and a half years respectively after they attacked Ekram Haque in Tooting, south London, last August.
Dominic Grieve yesterday said that, after a "very careful review", he did not consider the terms to be unduly lenient and would not refer the case to the Court of Appeal.
Mr Grieve said: "This was a shocking case, not least because this cowardly attack happened in front of the victim's granddaughter.
"I commend the sentencing judge who lifted the ban on naming the defendants in order to warn others who may be tempted to indulge in such appalling behaviour.
"The power to refer cases to the Court of Appeal is narrow and carefully defined.
"In this case the judge approached the sentencing exercise with care and, after looking at all the factors involved, I do not consider the terms to be unduly lenient and therefore I concluded that the Court of Appeal would be highly unlikely to increase the sentences."
Mr Haque cracked his head after being struck to the ground, suffering irreparable brain damage, and died a week later last August, the Old Bailey heard.
Elcock and Lyzai, both from Tooting, pleaded guilty to manslaughter and also admitted their parts in other assaults in which, the court heard, they had "targeted people for fun".
A third youth, aged 15, who cannot be named, was locked up for six months after admitting actual bodily harm.