His comments come less than 24 hours after comedy actor Volodymyr Zelensky — who plays a fictional president in a popular TV show — thrashed incumbent Petro Poroshenko in the first round of presidential elections.
The two largely pro-EU candidates are set to go head-to-head in a run-off vote on April 21.
The presidential elections marked the first national vote since Russia annexed Crimea in early 2014 and subsequently supported an uprising by pro-Russian separatists in east Ukraine.
"We are not interested in having a frozen situation in Donbass because it is in the interest of Russia. We need to get Donbass back, but we need to get Ukrainian Donbass back to Ukraine," Pavlo Klimkin told CNBC's Steve Sedgwick in Kiev, Ukraine on Monday.
"I would not say that it should be the same patterns or the same model for Donbass and Crimea but we need to get back both occupied territories."
"It is a fundamental point of Ukrainian DNA," Klimkin said.
Last month, Russian President Vladimir Putin traveled to Crimea to mark the fifth anniversary of the annexation of the region from Ukraine.
The Kremlin has spent heavily to try to integrate Crimea since 2014, including building a bridge to link the peninsula to southern Russia.
But, Western sanctions designed to punish Russia for its annexation have helped to isolate Crimea, driving up prices and slowing its development.
When asked whether he now reluctantly had to admit Crimea was permanently lost to Russia, Klimkin replied: "No, not at all."
"If you see what is going on in the sense of mood, in the sense of a change in mentality … It is a black hole in the sense of human rights."
"The people feel they are deprived of anything now in Crimea so let's see what is going to come in the sense of our common efforts. We need to show also that we are able to attract people, to show them that Ukraine is their future," Klimkin said.
In addition to a tense standoff in Crimea, Ukraine has endured five years of war against pro-Russian fighters in its occupied Donbass region. The fighting is estimated to have claimed the lives of approximately 12,800 to 13,000 people, according to the United Nations.
Ukraine has continuously pushed to keep its cause high on the international agenda, while pursuing membership of the European Union and NATO.
Successive rounds of economic sanctions on Russia goes some way to showing the West is still willing to support Ukraine. However, some external observers argue that a desire to prevent Moscow from interfering in other former Soviet republics could also be a root cause of the sanctions.
"Ukrainian military forces are completely different, now we have a real army," Klimkin said, before adding he was confident they were now able to "counter" Russian forces.