"We had three outstanding host candidates, who raised the bar and overwhelmingly demonstrated that they were all capable of hosting an exceptional Rugby World Cup", Beaumont said.
France has been chosen to host the tournament despite, last month, the Rugby World Cup board unanimously recommending to the World Rugby Council the selection of South Africa as the host nation. If World Rugby wants to encourage new hosts, it should be the other way around.
France got 24 votes to South Africa's 15 in the final round of voting.
"I would like to thank the Ministry of Sport and they gave a very important guarantee for the competition".
World Rugby had hit back at the criticisms of their process, labelling it inaccurate.
"In our letter, we had a great saying by Albert Einstein and here I paraphrase him: "There are a lot of things that can be counted which don't actually count and there are lots of things that count that can't be counted". We have to thank England who have supported us.
Ireland head coach Joe Schmidt remains convinced his side's record 30-3 thumping of the Springboks in Dublin on Saturday could swing the vote of World Rugby's member nations today, but that appears to remain a long shot.
"You would have thought [that they would support us] but the Scots went for the money and effectively said to us that they would vote for the bid that produces the most monies".
"It will be for the next generation of SA Rugby leaders to decide whether to compete for the 2027 tournament or beyond", he said. "When the Fifa World Cup was held there in 2010, we had a more than 20 percent uptake in players".
"We are bitterly disappointed at this decision and would like to apologise to the people and government of South Africa for raising their hopes", he said.
What is clear, though, is how hard hit South Africa's rugby development will be without the "golden ticket" of the 2023 hosting rights.
"We've won but it's really grass-roots rugby that has won", he added.
"We are disappointed today but we can look back with pride at the significant time and collaborative effort which had been put into our bid and which proved that Ireland has the credentials to host a Rugby World Cup".
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