He added that his daughter Grace, 6, was fine while their mother Nadine, 30, was still in hospital recovering from her injuries.
Darren Ferguson, who is manager of League One side Peterborough United, is estranged from his wife.
"This is a difficult time for myself and my family and we would ask for privacy for both ourselves and the hospital at this moment in time," he said in a statement on his club's website.
Cheshire Police said firefighters had to cut the children's mother from the wreckage of her Vauxhall Corsa after it collided with a Ford Fiesta at 8:25am on Tuesday in Macclesfield, northern England.
She was flown by helicopter to hospital while her children were taken to hospital by road ambulance.
Police said Grace had suffered minor injuries and that Charlie suffered more serious injuries without giving further details.
The 17-year-old male driver of the Fiesta was taken to hospital with leg injuries.
Newspapers reported Ferguson had considered returning from London where the semi-final was being played to be with his injured relatives, but decided to stay to oversee the game after being told their lives were not in danger.
Police appealed for witnesses to the crash to come forward.
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