Matty Kennedy first game for "Killie" in a 2–1 win over St Mirren at Rugby Park on 2 January 2012. He ended the 2011–12 campaign with 11 Scottish Premier League appearances. He played three games at the start of the 2012–13 season before leaving the club; manager Kenny Shiels expressed his concern that Kennedy had left Kilmarnock too soon and he had missed out on seeing Kennedy's "proper development" at the club. On 31 August 2012, the final day of the summer transfer window, Kennedy signed for English Premier League side Everton for a "nominal fee". The fee was later revealed to
Kenny Shiels several signings, the club, remained bottom of the league and a 2-0 loss against Alloa Athletic on 12 April 2014 confirmed relegation for Morton. Despite being relegated, it was initially believed that Shiels would stay on as the Greenock Morton boss for the next season, and attempt to return Morton to the Championship, similar to his experience during his time at Coleraine. However, Shiels resigned on May 2014 following a 10-2 defeat by Hamilton Academical which ended a poor season and relegation from the Scottish Championship. Immediately after the match, Shiels said in the post-match press conference, that he was