Jason Deeley-Brewer suffered burn injuries when the rocket hit and exploded on his leg.
It also burned a hole through his tracksuit bottoms. The 43-year-old, who had his three-year-old daughter on his shoulders, said he managed to stay on his feet, but was later taken to hospital for treatment.
The impact of the exploding firework can be seen by the burnt-out holes in the tracksuit trousers Mr Deeley-Brewer was wearing at the event on Wednesday night.
The father-of-five is still receiving treatment for the burns from a doctor.
He said he had planned to buy some fireworks for his own display, but following the incident, he had changed his mind.
He said: "The whole thing has made me reluctant to attend another firework display unless I'm absolutely sure my family and I are safe.
"The scary part for me was that I was with my daughter, and she could have been hurt, not me.
He was one of four people injured when the rocket shot through safety barriers at Brunswick Park in Wednesbury on Wednesday night.
He says he will now take legal action against event organisers Sandwell Council over his injuries.
Mr Deeley-Brewer, who lives in Wednesbury, was leaving the display with his daughter Lilly-Rose and partner Angela Walters when he was hit by the firework.
He said: "We stopped at the Brunswick Park main gates and I saw a big group of people ahead at the skate park, so I picked up my daughter and put her on my shoulders.
"As I did a stray firework came over the top of us and exploded on empty land nearby, then another firework hit my leg, exploding and burning through my trousers.
"There was a huge bang and a flash of green light – I managed to stay on my feet with my child on my shoulders, but saw a lad nearby fall to the ground and pass out."
He said officials had looked at his leg and was told he could go home.
"But when I got home my partner looked at it and said my leg was burnt with cuts and bruising. I went to hospital and they treated the burns before wrapping the leg up in dressing." He said: "I was lucky I picked up my daughter when I did, or she might have been hurt."
Councillor Elaine Costigan said council officers had met with the firework suppliers as part of their investigation. She said: "Lessons will be learnt."
Mr Deeley-Brewer has contacted solicitors to begin the process of a claim against Sandwell Council.
He claims the event was poorly organised and failed to protect the crowd of about 12,000 people. Three other people were hurt as a result of the stray firework.