The 28-year-old says there were "intense" negotiations between the two clubs prior to his transfer, adding he hopes a bigger stage helps his international prospects
The 28-year-old completed a £34 million move to the Etihad Stadium on Thursday, and the Brazil international says he remained in Ukraine following the end of the season to convince Shakhtar to reduce their demands and push the deal through.
"I'm relieved," he told Globo. "It was a big battle. The negotiations were intense, took several days and I even abandoned my vacation.
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"When the first offer came in, they said no. I insisted a lot in order to convince the manager, the board and even the captain.
"I had meetings with the president who promised he would talk with Manchester City if an offer of €40m [£34m] came, which finally happened.
"The truth is that I wanted to leave Shakhtar after eight years there. I told them this. As I was loved there, respected by the fans and within the club, they gave up.
"But I think they demanded such a high fee just to find out how much Manchester City wanted to sign me. Also, knowing Ukrainian culture, they were afraid someone would offer a lower fee and sign me."
Despite being 28 years old, Fernandinho was afforded an international debut just two years ago - since going on to make four more appearances for Selecao.
The defensive midfielder has admitted he hopes his move to the Premier League will boost his chances ahead of the Brazil-based 2014 World Cup.
"The national team was certainly something that I took into account when I made my decision," he added.
"I had a stable life in Ukraine. I had adapted and I was loved by the club. But I was left out of the national team in early 2012 and didn't get called up again. That really affected me.
"Then this chance to move to England came. I wanted to go as it will give me more visibility, both in Brazil and Europe. Now my chances of returning to the national team will certainly be a lot bigger."