It was originally feared that the Brazilian would miss over a month of action after injuring his shoulder on October 4.
But after returning for Saturday's win over Sheffield United, Alisson was full of praise for the physios who speed up his recovery.
"It's good to be back. I'm really happy. I try to give my best and I have the top physios on my side, helping me to accelerate the recovery process," Alisson said ahead of facing FC Midtjylland on Tuesday.
"As soon as the doctor told me it was four to six weeks, I told him 'no doc, we go to two or three weeks maximum!'
"He agreed with me, and then we just went for it. I'm really happy to be back, and I want to thank the physios, the fitness staff, the doctors and the goalie coaches who helped me on this process.
"It's bad not being involved in a football game. It's the worst thing for a player, but it's part of the job, injuries. We try to avoid them, but sometimes they happen. I'm glad it was only three weeks, but it was a long three weeks, more like three months!
"Being not involved is always hard, not only Atletico [Madrid] or Aston Villa. You want to help, you want to do what you love to do, help your teammates go for our goals."