"The president will be responsible for so many things, we'll have to see the actions that the president makes," said Moussa, calling an earlier "constitutional declaration" on the president's powers sufficient.
Many voters were unhappy with both choices in the runoff.
Morsi and Shafik are the most nonrevolutionary of all candidates and represent "two typically tyrannical institutions: the first (Morsi) being a member of the Muslim Brotherhood, and the second (Shafik) a senior official of the former regime," Sonya Farid wrote for Al Arabiya earlier.
"Everything about Egypt's revolution has been unexpected, and the first-round results in the country's first-ever competitive presidential elections are no different," Omar Ashour, director of Middle East studies at the University of Exeter and visiting scholar at the Brookings Doha Center, wrote for Project Syndicate previously.
Egypt's voters "overwhelmingly chose the revolution over the old regime ... but their failure to unite on a single platform directly benefited Shafik," Ashour said.
Thursday's rulings come a day after Egypt's military-led government imposed a de facto martial law, extending the arrest powers of security forces.
Egypt's Justice Ministry issued a decree Wednesday granting military officers the authority to arrest civilians, state-run Egypt News reported.
The mandate remains in effect until a new constitution is introduced, and could mean those detained could remain in jail for that long, the agency said.
Lawyers for the Muslim Brotherhood filed a court appeal against the decree on Thursday, the same day Clinton "expressed concern" about measures she said appeared "to expand the power of the military to detain civilians and to roll back civil liberties."
A decades-old emergency law that critics said gave authorities broad leeway to arrest citizens and hold them indefinitely without charges expired on May 31.
The political scene in Egypt remains tense after the parliament failed to agree on a committee to write a new constitution defining the powers of the president and the parliament.