Liverpool were eliminated from the 2014–15 UEFA Champions League after drawing against Basel in their final group match, dropping into the Europa League. The Reds were subsequently knocked out in the Europa League round of 32 after losing 4–5 on penalties to Turkish side Beşiktaş. On 19 April 2015, Liverpool were defeated by Aston Villa in the FA Cup semi-final. Liverpool finished the season with a 6–1 defeat to Stoke, finishing sixth in the Premier League. This meant Rodgers became the first Liverpool manager since the 1950s not to win a trophy after three seasons in charge. Despite this, Rodgers received the backing of Liverpool's owners.
On 4 October 2015, Liverpool played their 225th Merseyside derby against Everton with the game ending again in a 1–1 draw. This was the fifth time in Liverpool's previous six games that they had taken a 1–0 lead, then to have the game end in a 1–1 draw; while they had just one win in their previous nine games. Just one hour after the game, Rodgers was sacked, leaving Liverpool in tenth place after eight matches played. Later, it became known that the decision to sack him had already been made prior to the match against Everton. The following day, Rodgers released a statement through the League Managers Association stating, "I am, of course, incredibly disappointed to be leaving... [but] it has been both an honour and a privilege to manage one of the game's great clubs."
Rodgers separated from his wife, Susan, in the summer of 2014 and divorced in December 2015. The couple have two children – a son, Anton, also a footballer, and a daughter, Mischa. Rodgers got engaged to Charlotte Searle in February 2016, and they married in June 2017. On 6 March 2019, about a week after Rodgers became Leicester manager, thieves broke into his home in Glasgow, stealing family possessions and medals he won at Celtic.