UNHCR regional director Vincent Cochetel called the incident a “tragedy on an enormous scale”.
Nine survivors who were brought to Lampedusa by the Italian coast guard are believed to be from West Africa.
Initial reports on Monday suggested that at least 29 migrants had died after their dinghy overturned.
The UNHCR said the migrants had departed from Libya on Saturday in four dinghies.
Mr Cochetel said, “Europe cannot afford to do too little too late”, and called the tragedy, “a stark reminder that more lives could be lost if those seeking safety are left at the mercy of the sea.”
In November, Italy ended a year-long operation aimed at rescuing seaborne migrants.
Known as Mare Nostrum, it was launched in October 2013 in response to a tragedy off Lampedusa in which 366 people died. The aim of the mission was to look for ships carrying migrants that may have run into trouble off the Libyan coast.
There is no way of knowing for sure whether these men, women, and children would have been saved if the former Italian search-and-rescue operation known as Mare Nostrum was still running.
But having spent a week on board an Italian navy frigate, I can be sure they would have done their utmost to save as many lives as possible.
The EU’s Triton border patrol is not designed to do that. It cannot pre-empt trouble in international waters – it can only act when lives are immediately at risk.
The Italian operation was set up differently. The naval crews knew they had one single purpose – to prevent death. Some time back, EU leaders pledged that not a single life would again be lost as a result of these large scale tragedies at sea.
The European Union now runs a border control operation, called Triton, with fewer ships and a much smaller area of operations.
The UNHCR says almost 3,500 people died attempting to cross the Mediterranean Sea to reach Europe in 2014, making it the world’s most dangerous sea crossing for migrants.
More than 200,000 people were rescued in the Mediterranean during the same period, many under the Mare Nostrum mission prior to its abolition, and the UNHCR expects the figure to remain high in 2015.
In a speech before the European Parliament in November, Pope Francis called for a “united response to the question of migration”, warning that the Mediterranean could not be allowed to become a “vast cemetery”.