The council took over the running of Montague Centre car park in Liverpool Street last Saturday following complaints over the previous operators, CP Plus.
But the 120-bay car park was changed to a pay and display, rather than drivers paying at the end of their stays, which led to some users being fined for accidentally not paying for parking.
A spokesman for the council said the change to paying in advance was 'clearly advertised' in the car park and at every pay station, but the council appreciated regular users needed 'time to adjust'.
A 14-day grace period has been enforced, meaning those parking without a valid ticket will receive a warning, rather than a fine, up to Monday, August 17.
All of the fines issued since the council took control of the car park have also been cancelled.
The council spokesman said: “We took the decision to take over the running of the car park after the public frequently raised complaints with us about the private operators. We know that the first few days have not been ideal and apologise for not being clearer to customers about the change to a pay and display operation.
“For those who still prefer to park without knowing how long they will stay in the town centre, the free MiPermit app provides notifications to a mobile phone that a parking session is about to expire and allows customers to extend their stay on the go.
“Blue badge holders can also now park here for free for a maximum of three hours if their vehicle is parked in a designated disabled bay with a valid blue badge and clock set at the time of arrival clearly displayed.”
As well as changing the way tickets are purchased, the council also installed new machines, repainted the bays and offered up to three hours free parking for blue badge holders.