Guterres said European governments had yet to match the "gigantic effort" that the island and its people had made in trying to cope with the huge influx.
"It is amazing that on a small island, you are managing, whereas in a big Europe, with half a billion people, they are finding it so difficult," Guterres told Lesbos Mayor Spyros Galinos and other Greek officials. "We are always saying this crisis is manageable at the European level, but to be manageable, it needs to be much better managed."
Without a Europe-wide approach and an effective strategy in dealing with the influx, Guterres warned, criminal networks would continue to thrive. "When states are not able to organize the orderly movement of refugees, smugglers take charge, exploiting people further and adding to their suffering," he added.
Describing his island as frontline, Mayor Galinos said: "the main issue is not the numbers, but the lack of a European policy to respond." Nevertheless, he said, Greeks would continue to do whatever they could to address the crisis and combat smugglers, "who not only exploit the people, but who put their lives at continuous risk."
"Above all, we are all human beings," the Mayor added. "We must all recognize the position of these people because we might all find ourselves in this situation one day."
The majority of the refugees and migrants arriving on Lesvos are from Syria, Afghanistan and Iraq. The rest, about five per cent, are migrants and refugees from 21 countries as varied as India, Bangladesh, Togo, Niger, Columbia, Haiti and the Dominican Republic.
The Greek Coast Guard on Lesvos receives between five to 10 distress calls a day and then sets out to rescue people in overcrowded boats.
Deputy Harbour Master, Antonio Sofiadellis, a leader in the Greek Coast Guard effort that has saved between 240-400 refugee and migrant lives every day, said that more people are being packed onto the flimsy boats these days – around 60 when 50 used to be the limit.
"The engines are very cheap and the smugglers don't care that they don't know how to operate the boats. This is something no country in Europe has faced. If we weren't there to rescue them, half or more than half would drown. The boats capsize, some fold, when the floor breaks."