Brussels officials said the resignation of Sir Ivan Rogers meant the UK had lost a "professional" diplomat who had always "loyally defended" his Government.
In an explosive resignation email, Sir Ivan hit out at the "ill-founded arguments and muddled thinking" of politicians and said civil servants still did not know the Government's plans for Brexit.
Sir Ivan unexpectedly quit weeks after he sparked controversy by warning the Government that a post-Brexit trade deal could take a decade to finalise, and even then may fail to be ratified by member states.
The European Commission said it regretted the loss of a "very knowledgeable" envoy and indicated that Sir Ivan had been a tough negotiator in wrangles with Brussels.
Sir Simon Fraser, the former head of the Diplomatic Service, warned that Britain was losing one of its biggest experts on Europe months before "very complex" Brexit negotiations begin.
But prominent pro-Brexit MP Iain Duncan Smith suggested civil servants are now having to "tear up the rulebook" for how they normally operate to deal with leaving the EU.
Commission spokeswoman Natasha Bertaud paid tribute to Sir Ivan in Brussels.
She said: "We regret the loss of a very professional, very knowledgeable - while not always easy - interlocutor and diplomat who always loyally defended the interests of his Government."
Asked if his resignation shortly before the tough Brexit talks begin would cause problems, she said: "This is not something that we are going to comment on at this stage. Negotiations have not yet started and we are still waiting for the triggering of Article 50 to commence those negotiations."
Sir Simon told BBC Radio 4's Today programme: "He is a highly intelligent, knowledgeable and experienced official and one of the greatest experts, if I can use the expert word, that we have on European matters in the British Civil Service."
He went on: "I do think that his sort of in-depth knowledge and expertise is a loss as we go into what is going to be, as (Brexit Secretary) David Davis himself has said, a very complex set of negotiations."
Sir Simon, who left his post in July 2015, rejected suggestions that Sir Ivan was not tough enough in negotiations, including David Cameron's attempt to reshape Britain's relationship with the EU before the referendum.
The ex-diplomat insisted Sir Ivan "called a spade a spade" in his advice to ministers.
In his resignation letter, Sir Ivan criticised politicians and urged his civil servants to continue to challenge ministers and "speak the truth to those in power".
Sir Ivan wrote: "I hope that you will support each other in those difficult moments where you have to deliver messages that are disagreeable to those who need to hear them."
It emerged in December, as Theresa May met European counterparts at a Brussels summit, that Sir Ivan had passed on warnings from other EU members that negotiations on a trade deal could take a decade.
But former Tory leader Mr Duncan Smith suggested Sir Ivan's views were less relevant as EU member states will inevitably be feeding him their most hardline views before negotiations begin.
He told Today: "They are now having to accept and understand that we are leaving and that means therefore sometimes the views and the opinions of what you keep feeding back from various member states isn't actually sometimes quite relevant."
Mr Duncan Smith also suggested Sir Ivan had undermined his position by "going public" too often.
Jonathan Powell, Tony Blair's former chief of staff and an ex-diplomat, warned the Prime Minister against hiring a pro-Brexit successor to Sir Ivan.
Appointing a "patsy" who does not explain plainly what the other side is thinking will doom the Brexit negotiations to failure as ministers will be operating in a "fantasy land" about what is achievable, he told Today.
In the email from Sir Ivan, sent just before 1pm on Tuesday, he said he decided to step down early so his replacement can be in place when Article 50 is triggered by April and formal negotiations begin.
But it comes amid reports of tension between the senior diplomat and ministers because of his pessimistic views on Brexit.
Sir Ivan stressed the need for expert civil servants to play a central role in the negotiations and urged his staff to tell ministers the true opinions of the other 27 member states "even where this is uncomfortable".
He added: "Serious multilateral negotiating experience is in short supply in Whitehall, and that is not the case in the (European) Commission or in the Council.
"The Government will only achieve the best for the country if it harnesses the best experience we have - a large proportion of which is concentrated in UKREP - and negotiates resolutely.
"Senior ministers, who will decide on our positions, issue by issue, also need from you detailed, unvarnished - even where this is uncomfortable - and nuanced understanding of the views, interests and incentives of the other 27."
Sir Ivan also said the allocation of roles in the UK's negotiating team needs "rapid resolution" and hit out at assertions by some politicians that a free trade deal will be easy to negotiate.
In comments seen as a veiled swipe at International Trade Secretary Liam Fox he said: "Contrary to the beliefs of some, free trade does not just happen when it is not thwarted by authorities: increasing market access to other markets and consumer choice in our own, depends on the deals, multilateral, plurilateral and bilateral that we strike, and the terms that we agree."
The European Parliament's chief Brexit negotiator, Guy Verhofstadt, paid tribute to Sir Ivan, describing him as "a much-respected UK civil servant in Brussels who knew what he was talking about".
Theresa May is expected to appoint an EU ambassador who “believes in Brexit” in the wake of the current Brussels representative's decision to quit after being cut adrift by Downing Street.
A post-Brexit trade deal between Britain and the European Union might take 10 years to finalise and could still fail, the United Kingdom's ambassador to the bloc has told Prime Minister Theresa May's government, the BBC reported on Thursday.