Wa-ays Dhaye, 18, died from multiple knife wounds after being attacked in Thurston Street, Slough, in August.
He was walking home after spending the day at Notting Hill Carnival.
Khianni Gordon was jailed for life with a minimum of 19 years for murder while Kaneel Huggins and Antwon Clarke were given 10 and nine-year sentences respectively for manslaughter.
Gordon, 18, was also convicted of perverting the course of justice.
Clarke and Huggins' sentences were referred to the Court of Appeal by the Attorney General under the Unduly Lenient Sentence scheme.
Huggins, 19, had his sentence increased to 16 years, and Clarke, 18, had his sentence increased to 15 years.
Gordon's sentence was not considered by the court.
Speaking after the hearing, Attorney General Jeremy Wright said: "These offenders knowingly participated in the plan to assault and injure Wa'ays Dhaye knowing full well that really serious harm or death could be caused.
"Knife crime is a real scourge of our society and it's important that prison terms for this type of crime reflect the seriousness of the offending."
Mr Dhaye, who was born in Holland but lived in Slough for 10 years, was stabbed while walking home after spending August bank holiday at the Notting Hill Carnival. He died later in hospital.
Det Ch Insp Kevin Brown of Thames Valley Police, said the three had "hunted down" Mr Dhaye following a minor altercation between two groups at the carnival.
He said: "The three of them left Wa-ays dying in the street and it was members of the public who found him and came to his aid."
Update 21 November 2016: This story has been amended following updated information supplied by the Attorney General about the sentencing
Two men from High Wycombe jailed for a fatal stabbing have had their sentences increased by the Court of Appeal.