"I deeply regret this opposition and I do not see any reason for it," Guterres said at the annual World Government Summit hosted by Dubai.
Guterres described Fayyad, a former World Bank official with a track record of fighting corruption, as "the right person for the right job at the right moment".
"It's a loss for the Libyan peace process and the Libyan people," he added.
The UN leader on Wednesday had informed the Security Council of his intention to appoint Fayyad as a replacement for German Martin Kobler to conflict-torn Libya.
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But US ambassador to the United Nations Nikki Haley vetoed the appointment, saying Washington did not support the message the move would send.
Israeli Prime Minister Benjamin Netanyahu hailed the US veto of Fayyad as counter to the "free gifts constantly given to the Palestinian side".
Israeli media has meanwhile reported that the Jewish state could accept Fayyad's appointment if Tzipi Livni, a former Israeli foreign minister, were offered the position of UN deputy secretary general.
The head of the United Nations requires the unanimous support of all 15 Security Council members for appointments of special representatives to conflict areas.
Libya has been in turmoil since a 2011 revolution overthrew and killed longtime dictator Moamer Kadhafi.