And he insisted the TV star must have seen his daughter in the passenger seat.
Video footage shows how the pair exchanged an initial wave, before the dad shouted: "Unlucky Jamie lad!" and "2-1!"
"My biggest regret is for the 14-year-old girl to be caught in the middle of it", Carragher said.
He apologised on Twitter on Sunday, and said he was "goaded three/four times while being filmed" but there was "no excuse". I'm devastated for the family involved and my own family.
"Obviously I've had Sky Sports, family, and the people most affected are the family involved".
Carragher, who made over 500 appearances at the heart of Liverpool's defense but never actually won the Premier League, was driving from United's Old Trafford stadium where he had been providing expert commentary, when he was goaded by the fan.
Manufacturing, capital & consumer goods push IIP growth to 7.5%
Experts suggest the consistent growth in the industrial production could boost the overall economic growth in the fourth quarter. In terms of industries, 16 out of the 22 industry groups in the manufacturing sector showed positive growth in January.
Murphy said: "There is no way I can come on here, no matter how much I respect him, and say what he has done is not wrong".
"Because it is a young girl it feels slightly worse to me".
Hollywood actor Jones - who played for Wimbledon, Leeds and Chelsea - said Carragher is a "coward" and needs to "get down the job centre".
"Hopefully going forward I can show the real me".
Will he stay as a Sky pundit?
RadioTimes.com understands that a decision about Carragher's future at Sky has yet to be made.
Hokies lose huge 2nd half lead, fall to Notre Dame 71-65
Virginia Tech scored 9 consecutive points with 7:11 left in the 1st Half, making the game 27-17 in favor of Virginia Tech. Dating back to the 2011 season, Notre Dame has posted a 32-4 (.889) combined record at the Diamond 9 Citrus Classic.
"I don't know what will happen [long-term]", he told Danish paper BT, "It is not good behaviour but we are all just human beings".
JC: I called the family and they were upset and disappointed last night.
JC: A poor message not just the game of football but it's a poor message for everyone out there man, woman or children.
But they pulled the 40-year-old from their line-up and it is believed Sky Sports bosses have decided he will not appear on MNF with fellow pundit Gary Neville following crunch talks.
"I want to listen to his version", he said.
Kane injury leaves Pochettino 'concerned'
The Sun says Kane is in Real Madrid 's sights, even though the Spanish giants know he could cost in excess of £200million. His cross for Mustafi's opener made him the fastest man to 50 Premier League assists, taking 141 games.