The prime minister also claimed the UK would control “all the fish” in its coastal waters in years to come – even though the EU has the right to impose harsh retaliation if it tries.
“Unfortunately, the demand in restaurants on the Continent for UK fish has not been what it was before the pandemic,” Mr Johnson told an interviewer.
He was put on the spot after a protest over the impact of the Brexit fishing deal in London led to 14 people being issued with fixed penalty notices.
Lorries transporting freshly-caught produce have been held up at distribution hubs and many have struggled to enter into France.
Watch: Why is fishing so important in Brexit talks?
Some Scottish fishermen have taken to landing their catch in Denmark to avoid the “bureaucratic system” that exports to Europe now involve.
But Mr Johnson said that “insofar as there are problems at the moment”, they were “caused by teething problems, people not filling in the right forms, or misunderstandings”.
There would be compensation “when it's not people's fault”, but, the prime minister claimed: “Be in no doubt that there are great opportunities for fishermen across the whole of the UK.”
And he added: “In just five years’ time, five and a half years’ time, we will have access to all the fish in all of our coastal waters.”
However, as The Independent revealed, the Christmas Eve deal handed the EU the ability to shut off gas and electricity supplies if the UK tries to seize control of disputed stocks.
James Withers, chief executive of Scotland Food & Drink, said: “Anger amongst Scotland’s seafood exporters has been simmering for two weeks now as the door to their most important market has been slammed shut. Many now fear for their survival.
“We desperately need to press pause on the new bureaucratic checks on exports. We need time to get systems properly built as they keep falling down.”
The prime minister also repeatedly to say if the planned £1,000-a-year Universal Credit cut will go ahead in April, ahead of a Commons vote on the controversy tonight.
“What we have said is we will put our arms around the whole of the country throughout the pandemic,” he said.
“We have already done £280bn worth of support and we will keep all measures under constant review.”
And, on a visit to a Covid vaccine-manufacturing plant in Oxfordshire, he again promised the situation would look “very different by the spring”.
“We're getting it out as fast as we can, four million done so far, I think we've done more than half of the over-80s, half of the people in care homes, the elderly residents of care homes,” Mr Johnson said.
“That doesn't mean we are not going to be living with the consequences of the arrival of the coronavirus pandemic for a while to come – the economic consequences and the threat to our health as well.”
Watch: 10 ways to Brexit proof your finances