The Reds confirmed on Thursday that Benitez is to leave the club by mutual consent, bringing his six-year reign to an end.
And former Anfield boss Evans told Liverpoolfc.tv: "It's always sad when a manager leaves.
"Rafa was a good servant to the club over his six years and obviously successful. Unfortunately last season wasn't so good and there's been a lot of criticism.
"Sometimes as a football club you have to make a decision to take the club forward and that seems to be what has happened today."
During his stewardship, Benitez guided Liverpool to success in the Champions League and FA Cup, while also lifting the European Super Cup and Community Shield.
The Premier League title remained elusive, however, although the 50-year-old helped the Reds mount their strongest championship challenge since 1990 in 2008-09, with the team ending the campaign in second place having amassed 86 points.
Evans said: "The fans will always be grateful to Rafa. If you win the Champions League, the fans will always endear to you, and there was the FA Cup, Super Cup and Community Shield too.
"Fans will look back on Rafa's reign and say it was a great period, but unfortunately one year you can do poorly and that's the way football is today."