In the Daily Telegraph, Lord Hague said he was asked the question "for months... everywhere I went abroad" if "we would lose heart" about leaving.
He said he explained to them that "this really is a democracy".
Lord Hague also backed a "transitional" withdrawal from the EU saying it had "immense" attractions.
Lord Hague - who campaigned to remain in the EU - stood down as foreign secretary in 2014, and left the House of Commons in 2015.
He wrote in Tuesday's Telegraph: "The electorate voted to leave the EU, and therefore we leave.
"What is more, the number of people who voted to do so was higher than the number of votes cast for any government in our history.
"To me and many of my former colleagues in government who preferred to remain, the argument was over.
"In the recent general election, both main parties were clear that they were committed to the referendum outcome.
"Globally, the message has now got through."
But Lord Hague added that "just as the message was accepted, the voters pulled off another surprise and refused to give a majority to the ministers negotiating the exit" [in the general election].
He said there was the clear potential for Brexit to become the "greatest economic, diplomatic and constitutional muddle in the modern history of the UK, with unknowable consequences for the country, the government and the Brexit project itself".
And he said the Chancellor Philip Hammond deserved "great credit" for putting forward a possible solution.
Lord Hague said: "He has evidently been trying to persuade his cabinet colleagues that we should be seeking to stay in the EU single market and customs union during a transition and 'implementation' phase lasting to 2022, followed by a free trade deal with our former partners after that.
"This is seen by longstanding advocates of leaving as a 'soft' position or a climbdown.
"But in reality it is a plan to rescue Brexit from an approaching disaster."
Mr Hammond has said any transitional deal in the period after Brexit must end by June 2022, the time of the next general election.
But the chancellor said there must be "business as usual, life as normal" for Britons as the UK left the EU.
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The Real Madrid star left the pitch with a thigh problem following a clash with goalkeeper Kiko Casilla.
"It was a minor scare, a knock, but in a few days I will be well," said Ronaldo, who has 51 goals this season.
Real Madrid face Atletico Madrid in Milan this weekend in a repeat of the 2014 final, which Real won 4-1.
Portugal forward Ronaldo, 31, has been plagued by a thigh injury that forced him to miss three games in April.
He came off at half-time during Real's final La Liga game of the season.

The A9 drops from 150m (492ft) to 20m (65ft) as it enters a valley at the Berriedale Braes.
Caithness Chamber of Commerce said it was taking too long starting construction work on the improvements and the problem was being ignored.
Transport Scotland said it was continuing to progress the design work.
The A9 provides a link to the far north mainland coast and the ferry services at Scrabster, Gills Bay and John O'Groats to Orkney.
Chamber chief executive Trudy Morris said: "For too long, the Scottish government has ignored the impact the Berriedale Braes has on those living and working in the North of Scotland and Orkney Isles."
She added: "While progress has been made in identifying a solution to this important issue, we are disappointed that the Scottish government is dragging its heels in moving towards a practical implementation of this.
"The project as it stands is effectively shovel-ready - all that remains is for Scottish government to commit the funding."
Last year, the Scottish Chambers of Commerce called for work to tackle the bend to be accelerated.
Government agency Transport Scotland said a significant step in the project should be taken later this year.
A spokeswoman said: "We are continuing to progress the design work for the Berriedale Braes improvement scheme following the publication of draft orders last year.
"We are currently working to resolve objections to the scheme and subject to completion of the statutory process we will look to publish made orders later this year."
Made orders mark the last stage in the development of a final design for a new road.
Business leaders and politicians asked former Foreign Secretary William Hague how the UK would "get round" the EU referendum result, he has revealed.
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Cristiano Ronaldo says he will be fit to play in Saturday's Champions League final against Atletico Madrid after limping out of training on Tuesday.
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The Scottish government has been accused of "dragging its heels" on proposed improvements to a challenging hairpin bend on the A9 in Caithness.