The president, whose powers are limited by constitutional changes introduced at the height of the protests, has all but lost control of the legislative agenda since he appointed his rival, Viktor Yanukovich, as prime minister last year.
Beaten by Yushchenko in 2004 elections, Yanukovich staged a comeback after the president's "Orange Revolution" allies fared badly in a later parliamentary poll and were unable to form a government.
Yushchenko's popularity has sunk to single figures.
Only 196 parliamentarians in the 450-seat chamber backed Ohryzko, a career diplomat who had vowed to uphold Yushchenko's foreign policy, cornerstone of a liberal programme promised during "Orange Revolution" rallies.
Approval requires 226 votes.
The chamber later rejected the president's nominee to head the intelligence service, Viktor Korol.
Yushchenko, speaking in the southern region of Crimea, dismissed the votes as "a nursery game" and said he would submit both names again after consulting parliament.
"At issue here is the country's authority, its international standing," he said.
Yushchenko sees membership of the EU and Nato, both of which have expanded eastward to the borders of Russia and other ex-Soviet states, as a key element in building a transparent society with liberal aims.
Most Ukrainians have no objection to joining the EU.
But decades of Soviet criticism has made many suspicious of Nato and surveys show large majorities against membership, though Kiev has been co-operating with the alliance for years.