"We lost the flower of a generation and in the years to come it sometimes seemed that with them a sense of vital optimism had disappeared for ever from British life," William said at a ceremony in northern France.
"It was in many ways the saddest day in the long story of our nation," he added, speaking on the eve of the 100th anniversary of the start of the World War I battle in which some 20,000 British soldiers died on the first day alone.
William, his wife Kate and brother Prince Harry attended the start of an all-night vigil at the Thiepval memorial to honour the 1.2 million troops of different nationalities who were killed, injured or listed as missing.
Soldiers from the UK, France, Australia, Canada, Germany, India, Ireland, New Zealand and Pakistan took turns maintaining the vigil until 7:30 am (0530 GMT), the precise time that tens of thousands of troops clambered out of the trenches only to be mown down by German guns.
"Tonight we think of them... We acknowledge the failures of European governments, including our own, to prevent the catastrophe of world war," the prince, also known as the Duke of Cambridge, said.
In addition to around 20,000 British fatalities on that first day, tens of thousands more were maimed or wounded.
"It's quite emotional in a way. I feel it's important to remember these things," 73-year-old Irishman William Vernon said earlier as he arrived under rainy skies to attend the main commemoration ceremony on Friday.
Vernon said he was coming to remember his great-uncle -- also named William -- who died aged 26 in the battle. Like the 10,000 members of the public attending, he applied for his ticket online.
Vernon's son, William, 33, said he felt it was important to pay tribute to his relative who died "in the most horrendous conditions. It was an absolutely awful war, a pointless war. To be in the trenches was absolute torture", he said.
'I do not want to die'
Prince Harry read out a poem, while soldiers at the vigil read out letters from those who had fought in the battle.
"I do not want to die. The thought that I may never see you or our darling baby again turns my bowels to water," wrote Captain Charles May of the Manchester Regiment, who did not make it through the first day, in a letter to his wife.
Britain's Prince Charles will also attend the main ceremony at Thiepval on Friday, one of six in the Picardy region.
The Thiepval Memorial is the largest Commonwealth war memorial in the world, commemorating more than 72,000 missing servicemen.
British Prime Minister David Cameron -- mired in a battlefield of his own after Britain voted to leave the European Union -- will attend Friday's ceremony alongside French President Francois Hollande.
"Beyond what is happening at a European level, the United Kingdom remains a friend with which France wants to keep a relationship," a source close to the president told AFP.
Futility of war
The Battle of the Somme was launched on July 1 as Allied forces hoped to relieve the pressure on the French, who were racking up losses in Verdun, by attacking the Germans further north at the Somme.
However carnage ensued on both sides despite the frontline barely moving, in a battle that came to symbolise the horrors of trench warfare and the futility of the conflict.
"Imagine yourself, standing in a trench with water well over your knees... while thousands of unseen shells come shrieking and whining overhead. There is a very slight pause -- then it bursts and a tearing, rumbling blinding crash... hurling thousands of red-hot splinters in all directions, killing or maiming all they happen to strike," wrote Private Albert Atkins, who survived the war.
A century on, the eerily calm, bucolic fields belie the slaughter wrought there, and are now the haunt of tourists visiting war cemeteries and overgrown trenches.