Derbyshire police and crime commissioner Hardyal Dhindsa acknowledged some officers "may get it wrong" when enforcing England's coronavirus regulations and that people were becoming "fed up" with ongoing national lockdown restrictions.
He said officers had a "very difficult job in really trying circumstances" due to the "ever-changing" COVID-19 restrictions.
Jessica Allen and her friend Eliza Moore were fined when they drove separately from their homes in Ashby de la Zouch, Leicestershire, to a remote beauty spot in Derbyshire.
Mr Dhindsa said a review was looking at whether the officers had acted in error and added the force was "big enough to apologise".
"It's no wonder that in circumstances like this, sometimes when they are trying to do the best job they can, they may get it wrong," he said, speaking on BBC Breakfast.
"Having looked at [the incident involving the two women], listening to what I know, it looks as if we might have been able to deal with it differently.
"But it's an operational matter, I've asked the chief constable to review these cases and if the police acted in error, then the fines can be rescinded by them."
When asked if police being "overzealous" could put people off complying with coronavirus restrictions, he replied: "It could be."
But Mr Dhindsa said although there was much more traffic and activity than in the first lockdown in March, "in the main" the public were following guidance.
It comes as vaccines minister Nadhim Zahawi said the government did not "want to go any tougher" than the current lockdown rules, but suggested there could be a tightening of existing restrictions if people kept failing to comply.
Mr Zahawi urged people to "behave as if they've got the virus" over the next few weeks, as the most vulnerable are vaccinated against it.