Luke McCormick, 25, was desperate to sort out problems with his girlfriend and seen driving "like at an idiot" at around 90mph moments before he smashed into a car taking a family on a day out.
Arron Peak, 10, and his brother Ben, eight, died instantly while their father Phil, 37, who was driving, suffered serious injuries.
McCormick, the highly-rated Plymouth Argyle goalkeeper, admitted causing death by dangerous driving and being twice over the drink drive limit and was jailed for seven years and four months.
Mr Peak and his wife, Amanda, said they were "pleased that at last Luke McCormick decided to face up to the fact he has caused the deaths of Arron and Ben".
They added: "However, we are disappointed to discover that he will be eligible for parole after only three and a half years.
"In court his barrister spoke of the effect this case has had on Luke. We find this offensive.
"He will restart his life when he is still a young man. Our sons will never experience the things Luke has had.
"Phil will carry the scars of the incident for life. We will both carry the emotional scars forever."
Mr Peak and his sons, from Partington, Mancheser, along with three friends were on the M6 motorway on their way to a day out at the Silverstone race track when McCormick, who was returning south in a powerful Range Rover from a team-mate's wedding in Bolton, ploughed into them near the Keele Services in Staffordshire, at 5.45am on June 7th.
He told witnesses at the scene: "I am so sorry, I'm sorry. I just fell asleep. I fell asleep, I'm sorry."
Stoke-on-Trent Crown Court heard that hours before at the wedding of former teammate David Norris, McCormick was upset about emails and false allegations which had been posted on the social networking site Facebook about his fiancee, saying that she had been unfaithful.
McCormick was openly crying about it, and had exchanged texts and phone calls with his girlfriend during the day about it.
He downed beer and shots of sambuca, and had just two hours sleep before, at 4.30am, he decided to go to Coventry to "sort out his love life".
He ignored telephone requests from his room-mate to pull over at services.
Judge Paul Glenn told McCormick: "You prioritised your own perceived needs, including, it seems, sorting out your love life over the safety of other road users.
"There was no good reason why you couldn't have stayed in that hotel for a few more hours to get the rest you needed... you chose not to do that."
Mr and Mrs Peak cried silently as sentence was passed, while other members of their family, who had confronted McCormick, a former England youth international once tipped to play in the Premiership, as he arrived at court, punched the air and shouted "Yes".
In a victim statement submitted to the judge, Mrs Peak and her husband Phil Peak, told how their lives had been "totally devastated" by the deaths of their sons. The couple wrote: "Our whole lives have been shattered... all our hopes and dreams for the future have been taken away from us."
Both Ben and Arron were huge Manchester United fans. The family received a personal letter of condolence from club manager Sir Alex Ferguson shortly after the boys' death.