The former boxer had been a vocal critic of his son's bout against Benn but accompanied him to the fight last weekend – much to the delight of the crowd at the Tottenham Hotspur Stadium.
Speaking on his YouTube channel, Eubank said: "I'm welling up now.
"A moment of a lifetime. It looks like it has been orchestrated by a director, for the car to pull up where it did, for me to be on the left-hand side of the car.
"For me to push the door open and put one foot down and there is the world's media. I chuckled.
"I was directed spiritually, I'm good but I'm not that good, that is why it moved the nation and the world."
Eubank Jr was admitted to hospital after the brutal bout and his father explained how accompanying his boy in the ambulance brought back memories of his fight with Michael Watson in 1991, when his opponent suffered brain damage.
He said: "My son junior is very proud and his face looked like a blown up football, almost twice the size.
"He will never let you see that but it brought me back all of those years to think about what Michael went through and I was feeling all that.
"People don't know but my son was touch-and-go and the only way we are going to know if he is going to be OK is with the CT scan.
"He suffered mostly in the hospital because of dehydration, even though the beating was severe. That is why he was in such discomfort for 24-30 hours."
Eubank is proud of how his son boxed against Benn but doesn't want him to risk his health again in a rematch.
The former world champion said: "The fight was extraordinary, I never thought I would see this type of performance from my son. From rounds six to 12 he stayed in the pocket which is where you are standing toe to toe.
"I'm so proud of that boy of mine and I'm so proud of Conor Benn and it will echo into eternity.
"(But) I don't want my son to go through that again. He doesn't know his life was in the balance and neither does he care."