James Gilbey, 25, from Leeds, died when he was hit by a car while crossing Stanningley Bypass in July.
Two men who were racing in cars on the road were later jailed for eight years each.
Richard Gilbey said: "Imposing such a lenient sentence just kicks us in the stomach even further."
Mr Gilbey, from Wiltshire, handed in a petition with about 12,000 signatures to Downing Street calling for a charge of manslaughter rather than dangerous driving when death is caused by racing.
Currently the maximum tariff for death by dangerous driving is 14 years, whereas the maximum sentence for manslaughter can be life imprisonment.
The government has said it recognises "public concern about sentencing" for such offences and is holding a consultation on penalties that ends on 1 February.
Majid Malik admitted causing death by dangerous driving. Kaiz Mahmood was found guilty of the same offence at Leeds Crown Court.
The court heard how the pair used the road as a race track and both drivers, who were from Bradford, reached speeds of nearly 80mph.
Mr Gilbey, from Bramley, Leeds, died at the scene when Malik's car struck him.  Mahmood's car did not hit the victim but he was found equally culpable.
Judge James Spencer QC described the racing as "madcap" and said "neither of you had the guts to stay".
Mr Gilbey said: "I wasn't there for James when he really needed me the most, knowing that breaks my heart".
He said the men may serve only half their sentence in prison and thinking the judicial system put that "value on his [son's] life was heartbreaking".
The father of a man killed in a "madcap" hit-and-run crash has petitioned the government for tougher sentences for drivers who kill.