"There are a lot of lessons to be learnt," Taoiseach (Irish PM) Micheál Martin has said after Brussels reversed its threat to put checks on the Irish border.
This came as part of EU efforts to control vaccine exports, amid dose shortages in the bloc.
People had been "blindsided" by the row but insisted the EU's move was "not an act of hostility," Mr Martin said.
The UK says it is confident the EU will not block vaccines entering the UK.
International Trade Secretary Liz Truss said the president of the European Commission Ursula von der Leyen had assured Prime Minister Boris Johnson that "there will be no disruption of contracts that we have with any producer in the EU".
Speaking to the BBC's Andrew Marr programme, she added that she was "very pleased" the EU stepped back from its plan to implement the border checks.
"What I want to do now is work with fellow trade ministers to keep these supplies open and to move away from the idea of vaccine nationalism and protectionism which we know simply harms our global health efforts and harms our global economy."
Speaking on the same show, Taoiseach Mr Martin said he first became aware of the EU's plan to put checks on the Irish border when the commission issued a public announcement.
He said he immediately contacted European Commission President Mrs von der Leyen and "articulated the very serious implications the move would have" - and that Mrs von der Leyen "took on board" his concerns and "thankfully" the commission pulled back from its stance.
Mr Martin added that the commission should have spoken to him first and said there were "a lot of lessons to be learnt" from the incident and that issues with the border between Ireland and Northern Ireland needed "fine-tuning".
Acknowledging the tension between the EU and vaccine manufacturer AstraZeneca was "terrible", he stressed the need for all sides to "calm down" and "dial down the tone".
However he also noted that there had been "shock" in the EU when "it emerged the original commitment [by AstraZeneca] of delivering 100 million doses wasn't going to be realised."
Earlier this week AstraZeneca's chief executive, Pascal Soriot, said the contract with the EU obliged the company to make its "best effort" to meet EU demand, without compelling the company to stick to a specific timetable.
This comes as the World Health Organization said "vaccine nationalism" could prolong the pandemic and further widen global inequality.
Ms Truss told the BBC: "This is a global problem that needs global solutions and what we want to do is help other countries, including the developing world get the vaccines they need to make sure the whole world is vaccinated."
The EU's threat of border controls came amid a deepening dispute over delays to the production and distribution of Covid vaccines across the continent.
The bloc is introducing a so-called transparency mechanism, which gives countries in the bloc powers to deny authorisation for vaccine exports if the company making them has not honoured existing contracts with the EU.
The EU's attempt to apply measures to the Irish border was widely-condemned, and the heads of the UK- and Europe-wide industry bodies have warned against export bans.
Former prime minister Tony Blair said the EU's threat was "a very foolish thing to do and fortunately they withdrew it very quickly".
"Companies are working as fast as they can to protect everyone. Export restrictions do no one any good and we urge governments to avoid them," Richard Torbett, head of the UK's Association of the British Pharmaceutical Industry, and Nathalie Moll, head of the European Federation of Pharmaceutical Industries and Associations, wrote in the Observer.
The EU has insisted that its controls are a temporary scheme, and not an export ban.
On Saturday Cabinet Office minister Michael Gove said the government expected vaccines manufactured by Pfizer and AstraZeneca to be supplied to the UK but said it would work with the EU to "make sure that their own problems can be tackled".
"Our first priority is vaccinating people in the United Kingdom, but we also want to work with our friends and neighbours in the European Union in order to help them as well," he said.
By Naomi Grimley health correspondent
Like many rich countries, the UK has bought more vaccines than it needs in order to hedge its bets in an emergency.
That's led some to argue that the UK should consider donating some - either to a neighbouring EU country such as Ireland which does not have such a plentiful supply or to poorer countries which currently have none.
But ministers say it's too early to make that call yet.
The World Health Organization wants richer countries to commit to donating their excess once they have enough to vaccinate their most vulnerable.
Norway has said it will do this and India has already given some vaccines to Nepal, Bhutan and Bangladesh in what's been called "vaccine diplomacy".
The UK government said a further 587 people had died within 28 days of testing positive for coronavirus as of Sunday, taking the total deaths by that measure to 106,158.
There have been a further 21,088 lab-confirmed cases of the virus in the UK, while 8,977,329 have received their first dose of a vaccine and 491,053 have been given the second dose.