Slot has parted ways with the club despite the Dutch coach guiding them to both Premier League glory and UEFA Champions League qualification during his two-year spell at Anfield.
The 47-year-old, who succeeded Jürgen Klopp in 2024 after the German stepped down following nine years in charge, enjoyed a remarkable start to life on Merseyside.
Slot led Liverpool to their 20th league title in his first season, with the Reds clinching the championship at Anfield in front of their own supporters and securing the crown with four matches to spare.
"It was made even more meaningful because you got to enjoy it with us, said Slot via the Liverpool Echo.
"Singing our songs, cheering the goals. And on the day we lifted the trophy, you were there - lining the streets outside the stadium, filling Anfield in anticipation.
"Having had much of that taken from you in 2020, it was never lost on me how much it mattered that you were part of it all.
"Seeing you come together in your hundreds of thousands on the streets of Liverpool for the title celebrations only reinforced that idea.
"Liverpool's 20th league title belongs to all of us and it will remain an important chapter in its history. For that we should all be proud.
"This club will always judge itself by the biggest honours. That is how it should be."
However, fortunes changed this season as Liverpool finished fifth in the Premier League, ending the campaign 25 points behind champions Arsenal. The club also suffered 20 defeats across all competitions, prompting Liverpool's hierarchy to make the decision to part ways with Slot.
Liverpool are expected to open formal discussions this week with Andoni Iraola regarding the vacant head coach position.
In the open letter, Slot thanked supporters for their backing throughout his tenure. He said the fans made him feel welcome from the moment he arrived and credited them for helping him through his time at the club.
"I leave with complete confidence in what lies ahead," said Slot.
"The players who have given so much to this club, who have upheld its values and helped create so many unforgettable moments, have built foundations that will endure."
"Securing Champions League football was an important responsibility and one that ensures Liverpool can continue competing at the highest level next season and beyond," he added.
"Change is part of football, but I know that this club will continue to make its people proud.
“When I first stood beneath that sign in the Anfield tunnel, I knew what this club demanded. I leave knowing we never stopped striving for it.”