Emad Al Swealmeen, 32, detonated a homemade bomb outside the hospital just before 11am on November 14, killing himself and injuring taxi driver David Perry.
According to police, the bomb used was a homemade explosive with ball bearings attached.
Security guard Darren Knowles witnessed the explosion and Mr Perry’s escape from the vehicle.
Mr Knowles told BBC North West Tonight that when he first saw the explosion he thought there was a problem with the car because there was so much smoke.
“I just thought it was a malfunction with the car and just ran over and see if he was all right,” he said.
The taxi driver told him: “Been blown up, been blown up. There’s a bomb in my car.”
He said that Mr Perry had realised the threat when he saw a red light on Al Swealmeen’s vest. “That gave it away for him to do something and he acted very quickly and very bravely,” Mr Knowles said.
He added that he had to stop Mr Perry from going back to his burning car, and instead held him in a “big hug”.
He said he was shocked that the explosion had happened at a children’s hospital.
“You don’t expect that to happen at a kids’ hospital where there are new-born babies.
“There’s no need for that.”
It comes as police have finished searching a property on Rutland Avenue in relation to the attack.
A cordon put in place in the area has now been lifted, Counter Terrorism Police North West said in a statement.