Jota died alongside Andre after their vehicle veered off a motorway in northern Spain before bursting into flames.
Jota joined Liverpool in 2020 after excelling for fellow Premier League club Wolves and was part of last season's Premier League-winning squad.
He was also an FA Cup winner with the Reds, as well as a two-time Carabao Cup winner.
In the statement, released via Liverpool's official website, Slot said how he was struggling to put into words his feelings of sadness surrounding the tragedy.
"What to say? What can anyone say at a time like this when the shock and the pain is so incredibly raw? I wish I had the words but I know I do not.
"All I have are feelings that I know so many people will share about a person and a player we loved dearly and a family we care so much about.
"My first thoughts are not those of a football manager. They are of a father, a son, a brother and an uncle and they belong to the family of Diogo and Andre Silva who have experienced such an unimaginable loss.
"My message to them is very clear - you will never walk alone. The players, the staff, the supporters of Liverpool Football Club are all with you and from what I have seen today, the same can be said of the wider family of football.
"This is not solely a response to tragedy. It is also a reaction to the goodness of the people involved and the respect that so many have for the boys as individuals and for the family as a whole.
'The shock is absolute'
"For us as a club, the sense of shock is absolute. Diogo was not just our player. He was a loved one to all of us. He was a teammate, a colleague, a workmate and in all of those roles he was very special.
Jota, Slot said, epitomised Liverpool's spirit: "I could say so much about what he brought to our team but the truth is everyone who watched Diogo play could see it," he said.
"Hard work, desire, commitment, great quality, goals. The essence of what a Liverpool player should be.
"There were also the parts that not everyone got to see. The person who never sought popularity but found it anyway. Not a friend to two people, a friend to everyone. Someone who made others feel good about themselves just by being with them. A person who cared deeply for his family.
In a particularly poignant recollection, Slot remembered their final conversation where he had congratulated Jota on his recent Nations League triumph with Portugal and wished him well ahead of his wedding.
"The last time we spoke, I congratulated Diogo on winning the Nations League and wished him luck for his forthcoming wedding," the statement continues.
"In many ways, it was a dream summer for Diogo and his family, which makes it all the more heartbreaking that it should end like this.
'One of the first songs I knew'
"When I first came to the club, one of the first songs I got to know was the one that our fans sing for Diogo. I had not worked with him previously but I knew straight away that if the Liverpool supporters, who have seen so many great players over the years, had such a unique chant for Diogo, he must have special qualities.
"That we have lost those qualities in such terrible circumstances is something we have not yet come to terms with. For this reason, we need everyone at the club to stand together and to be there for one another. We owe this to Diogo, to Andre Silva, to their wider family and to ourselves.
"My condolences go to Diogo's wife, Rute, their three beautiful children and to the parents of Diogo and Andre Silva.
'His name is Diogo'
"When the time is right, we will celebrate Diogo Jota, we will remember his goals and we will sing his song. For the time being, we will remember him as a unique human being and mourn his loss. He will never be forgotten."
Slot then signed off with the evocative line: "His name is Diogo."
Tributes have been pouring in since the news of Jota's passing broke this morning, with the footballing world in mourning.
Former boss Jurgen Klopp, who brought Jota to Liverpool in 2020, spoke of "a fantastic player, but also a great friend, a loving and caring husband and father," while former and current players have posted their condolences to his family.