Mac Allister completed his move to Anfield on Thursday.
In an open letter to Brighton, Mac Allister wrote:
"It's time to say goodbye to the club that opened the doors for me and gave me such amazing moments. I never thought I was going to live what I have lived in these three-and-a-half years, but this club gave me that opportunity and I'll be forever grateful.
"First of all, I'd like to thank every person who was a part of this journey, Tony Bloom, Paul Barber and my managers, Graham [Potter] and Roberto [De Zerbi] and all their staff; and most importantly, the players, who I have beautiful memories with and have learnt so much from.
"Thanks to everyone who works at the club who are the least seen but who work the hardest, so we can enjoy everyday and the team can achieve big goals. Finally, a special mention to all the fans, your support and respect during this time has been incredible.
"Your welcome after the World Cup, I will never forget it. I don't have any doubts that this team is going to achieve many important things, because they have the football skills and human quality to do it.
"I'll always watch you and support you (except when I play against you!). THANKS A LOT SEAGULLS! You will always have a special place in my heart!"