The celebrity hairdresser was eliminated from the show after picking up five votes from his fellow competitors.
His closest rival was Sean Maguire, who received three votes. Amy Williams and Angellica Bell each got one vote, while the other contestants did not receive any.
Clarke, who had admitted before the result was revealed that he didn't want to go home, confessed that he was upset by the decision.
"My pride's been really, really knocked, and that doesn't happen to me very often," he said. "Maybe that's what I needed, but I'm genuinely hurt."
Meanwhile, Clarke's teammates accused the other group of ganging up on him, with Lisa Maxwell calling the result "one heck of a coincidence" and Martin Kemp describing the vote as a "conspiracy".
"They knew that Sean was vulnerable and they obviously got together and that was the only way they were going to save him," Kemp said. "And they did."
However, Maguire claimed that the result was "just bad luck on Nicky's part", adding: "It could have very easily been me, but my team kind of kept me out of it. I'm happy with the way things have turned out. I'm feeling pretty chuffed."
71 Degrees North continues on Tuesdays at 9pm on ITV1.