Germany was represented by President Joachim Gauck, who took his place alongside world figures including US President Barack Obama and United Nations Secretary General Ban Ki-moon.
Although Merkel wrote in a book of condolence in the South African Embassy in Berlin on Monday, she did not travel to pay personal tribute, a decision which was criticized by some.
"For Germany it would have been the right signal," wrote Dagmar Dehmer in the Tagesspiegel newspaper.
The US was represented by four presidents, Dehmer noted - Obama was joined by George W. Bush, Bill Clinton and Jimmy Carter.
And the UK sent not only Prince Charles but also Prime Minister David Cameron.
It would be difficult to imagine that Merkel intended to suggest she did not care about Africa, or that Mandela was not special to her, Dehmer said.
But her absence was a mistake, she added. "That the supposedly most powerful woman in the world ignores this date without comment is the wrong signal. It shows a lack of empathy, a lack of humility and a lack of friendliness. More than a shame."
Around 90 heads of state and government leaders attended the ceremony in a football stadium, where Mandela was compared with Mahatma Gandhi, Abraham Lincoln and Martin Luther King.
Obama shook hands with Cuban President Raul Castro, which was greeted around the world as a sign of hope for possible reconciliation between their countries.
Mandela died on Thursday aged 95 after a long illness. He will be buried on Sunday.