Mr Coveney made the comments after the David Davis announced he had resigned as the UK's Brexit Secretary in the late hours of Sunday evening.
The two departures seemed to shatter May's own proclamation of cabinet unity last Friday, when she said she believed she had, after two years of wrangling, secured agreement on Britain's biggest foreign and trading policy shift in nearly half a century.
Coveney said nobody should be fooled into thinking both sides were close to a conclusion in the negotiations.
The resignations have fostered a deep distrust among many eurosceptics in her party, undermining her position and casting doubt over the Brexit process.
Barnier said outstanding issues included data protection, cooperation between police and judicial authorities and how to settle legal disputes that may arise under the withdrawal deal. "That dream is dying, suffocated by needless self-doubt". She appointed in his place Jeremy Hunt, an ally who voted to remain in the European Union in the 2016 referendum. Instead Britain will pay regard to its decisions in areas where common rules are in force. "In that respect we are truly headed for the status of colony".
On the worldwide markets, sterling slipped by a third of a cent against the dollar to $1.3288 in early trading.
Davis had earlier called May's plan risky and said it would give "too much away, too easily" to European Union negotiators.
He was joined by one other minister in his department, Steve Baker, and there are many reports that Suella Braverman has also quit.
It was a rocky day for May, weakened after she lost the Conservatives' majority in parliament in an ill-judged election a year ago. To what extent the position wins support from pro-Brexit MPs and others remains to be seen.
The UK would have "the freedom to strike new trade deals around the world" - something Mrs May will stress in the face of claims by critics that the plan for alignment with Brussels on goods will curtail the ability to reach agreement with countries such as the US.
The prime ministers plan for a soft Brexit was pushed forward by May at a crunch cabinet meeting at her countryside manor, called Chequers, on Friday.
He told BBC Radio 5 Live's Pienaar's Politics: "I'm very, very disappointed with the offer that we've seen coming out of Chequers - I'm disappointed that so-called Brexiteers in the Cabinet didn't pick up the cudgels and fight for a better offer".
"Over that time, I've listened to every possible idea and every possible version of Brexit".
Mr Gove told the BBC her plan was a compromise.
She said there was a "willingness to sit down and talk" about the plans.
But even if there is an agreement at home, May will then have to get the support of the European Union, which poured cold water on her earlier suggestions for customs arrangements.
"Politicians come and go but the problems they have created for people remain", he tweeted.
Now Johnson and Davis have jumped ship, and more officials might follow.
"It seems more and more that Britain will have to ask for an extension of the two-year period for Brexit negotiations", said one European Union diplomat involved in the talks.
They fear a clean break would cost jobs.
Britain would also be able to control its own tariffs and develop an independent trade policy, and the jurisdiction in Britain of the European Court of Justice will come to an end.
Officials in the bloc have repeatedly warned that Britain can not "cherry pick" benefits of membership, such as access to the customs union and single market, without accepting the responsibilities that come with being in the bloc, including allowing free movement of EU citizens to the United Kingdom.
"This is not a betrayal ..."
"The EU has always said that once Britain softens its red lines ... that they would also show some generosity and flexibility but I think there will be limitations to that flexibility".
Michael Gove admitted the agreement thrashed out after a marathon day of talks on Friday was not everything he had hoped for, but the environment secretary said he was a "realist" and recognised the need for compromise.