Paul Richards suffered a punctured tyre when his Volkswagen hit the steel edge of the pavement on the way out of Merchant Gate, next to Westgate Station, in September.
He had to fork out £140 for a new tyre after Wakefield Council, who run the car park, denied liability.
But Mr Richards, 69, said the pavement's edge and the position of a pole on the opposite side, which the council says is in place to protect pedestrians, is hazardous and could cause a serious accidents if a puncture goes undetected.
Pictures he took at the scene suggest many other drivers have hit both the pole and the pavement, in trying to squeeze through the narrow gap between them.
Mr Richards, a retired chemistry teacher from Aberford, said: "I realised on my way out that I'd hit it, so I stopped just outside the car park, and I was shocked to see that it hadn't just damaged the alloy of the wheel, but it had actually slashed the tyre as well.
"The exit is really tight and to avoid the pole you really have to exaggerate the swing to the right. It's very difficult.
"The position of the pole where it is is totally inappropriate.
"Looking at the amount of scratches on it, it could have been hit dozens and dozens of times."
Mr Richards said he couldn't understand why the edge of the pavement is steel, rather than concrete, which would be less likely to cause a puncture.
He added: "The danger is someone might have punctured their tyre, not realised it and then if it bursts on the motorway it could cause a fatality."
Mr Richards wrote to the council to complain shortly after the incident, but his insurers later told him they'd denied responsibility and insisted he'd lined up "incorrectly".
He says the issue has put him off using the car park again, despite its convenience for train travel.
Mr Richards added he was not highlighting the case in a bid to recoup the cash he'd spent on the tyre, adding: "Rather than having the money back it would just be really great if they changed it, so other drivers don't have the same trouble."
Gary Blenkinsop, Wakefield Council’s service director for the environment, said: “The safety of everyone who uses our car parks is our priority.
"The bollards near the exit of the car park were installed to protect car park users and pedestrians exiting the car park on foot from level one.
"The car park floor is yellow hatched illustrating the traffic lane for vehicles and guides drivers safely to the exit."
Local Democracy Reporting Service
An earlier version of this story incorrectly suggested Mr Richard's tyre was punctured by the pole, rather than the pavement. We have amended the article to reflect this and apologise for the error.