The former Labour leader apologised after attending a dinner party for nine, despite the Government's rule of six, which was introduced last month.
Boris Johnson's father was also forced to say sorry after being pictured without a face covering in a shop.
Both pictures emerged after fines for a first time offence of failing to wear a mask or flouting the rule of six was doubled to £200.
When asked about Mr Corbyn breaking the rules, Mr Eustice told Sky News that police should decide the appropriate action.
He said: "I think that the police will look at this and take a proportionate approach.
"What generally happens is you get a small number of fines of people persistently and deliberately breaking the law," he said. "In most cases, you will get guidance - a warning or direction to change you're approach and that is sufficient."
Pressed on whether Mr Corbyn should get a warning, he added: "We have the rule of six and it should be enforced but that doesn't mean there should be a penalty in every case.
"Sometimes it can be a warning. Sometimes people make mistakes and apologise for it. Sometimes it is clear there has not been a willful breaking of the law."
Mr Eustice later said the police should also decide if the Prime Minister’s father should be fined.
But he stressed that punishments should only be handed out to those showing a “wilful and reckless” disregard for the restrictions regarding face coverings.
Speaking to BBC Radio 4’s Today programme, Mr Eustice said: “The police will decide what approach they should take (with Stanley Johnson) but the appropriate response is to act in a proportionate and pragmatic way.
“They are only using fines as a last resort where you have wilful and reckless disobedience of the regulations we have in place.
“As a general rule, whether it is on public transport or in other venues, it will be a matter of either directing people to comply with the rules or to leave the premises or to leave public transport and that is the approach that is working most effectively.
“I think in both these cases, the (sic) leader of the Opposition (Jeremy Corbyn) and the Prime Minister’s father, in both cases they have admitted to making an error and have apologised for doing so.”
Ms Burley also asked the Environment Secretary what he would have done if he were in the same situation as Mr Corbyn.
Asked if he would go to a dinner party if there were omre than six people, he said: "I wouldn't, no."
"And if you got to a dinner party and there was more than six people there you would leave?" she continued.
"Yes," he replied.
"But you are surprised that the former Leader of the Opposition didn't do that?" Ms Burley asked.
Mr Eustice said: "Look it's for him to make that decision. Maybe he didn't realise what the rules were"
"What he can't count to six?," she asked.
"That's quite possible, I don't know," he replied. "The point I'm making is that, yes, that is obviously a breach of the rules but it is for the police to decide whether or not action is appropriate. In all of these things, we use enforcement when there has been a willful breach of the law, done on purpose, done repeatedly.
"Usually a warning is sufficient to get people to comply."
Introducing the higher fines last week, Mr Johnson said: "These rules, these measures will only work if people comply. There is nothing more frustrating for the vast majority who do comply, the law-abiding majority, than the sight of a few brazenly defying the rules."