Diaz's mother was rescued within hours of her capture by a Colombian guerilla group on October 28, but the search goes on for his father Luis Manuel Diaz.
After heading in a stoppage-time equaliser to prevent Liverpool suffering a shock defeat at Luton in a 1-1 draw on Sunday, Diaz displayed a t-shirt saying "freedom for Dad".
"It says a lot about his character, his strength, not many people imagine what he is going through," Alisson told Sky Sports.
"We are supporting him, we feel his pain but for him it is a different level.
"Football sometimes in dark moments can bring joy. Football is bringing a slice of joy to Lucho in this moment.
"He came, trained, came to the game and scored a fantastic goal for us. We are with him."
Brazilian international Alisson suffered his own tragedy in February 2021 when his father died in a swimming accident.
And he said he knew from personal experience the release that playing can offer.
"Football always surprises us in a good way. It happened with me when I was going through a difficult moment.
"When you are on the pitch you are focused on doing the job."
