The former Sierra Leone tactician was dismissed on Thursday after 15 months in-charge of Amavubi.
McKinstry said he was "surprised and disappointed" and the reasons "had not been made fully clear" to him.
McKinstry took over the Rwanda job from Englishman Stephen Constantine who stepped down in March 2015.
The Northern Irishman then led Rwanda to the quarter final stage of the 2016 Africa Nations Championship that they hosted.
He also led the team to the runner-up spot in the 2015 Cecafa Senior Challenge Cup in Addis Ababa, Ethiopia.
"The specific reasons behind the decision have not been made fully clear to me given our performance to date, I am therefore both surprised and disappointed by the announcement today, and that myself and the team will not be able to finish what we started," he said.
The 30-year old coach managed to record 11 wins, two draws and a dozen defeats in the 25 games he was in charge of Rwanda.
According to the Rwanda FA, McKinstry was sacked because he did not achieve some of the targets that had been set for him.
The FA announced former international Jimmy Mulisa, who had been McKinstry's assistant, as Rwanda's interim coach.
Mulisa was a key part of the Amavubi side that featured in the country's first and only Africa Cup of Nations finals in Tunisia in 2004.
Northern Ireland-born Johnny McKinstry has expressed his surprise after he was sacked as head coach of Rwanda's national team.