Mr Robinson said: "The violence and destruction visited on the PSNI is a disgrace, criminally wrong and cannot be justified.
"Those responsible are doing a grave disservice to the cause they claim to espouse and are playing into the hands of those dissident groups who would seek to exploit every opportunity to further their terror aims."
He said some demonstrators were employing language borrowed from the republican handbook to demonise police and undermine the DUP through a call for direct rule from London.
"All right-thinking unionists will want to channel their energies into political activity and to support the cause of finding political solutions to the problems that we face," Mr Robinson said. "In Northern Ireland the ballot box has primacy and is the only vehicle for choosing the people's representatives."
Police in east Belfast were dealing with serious public disorder in the Castlereagh Street and Templemore Avenue areas.