Mignolet signed for Liverpool in a £9 million deal yesterday.
Di Canio told safc.com: "Simon is a fantastic footballer, a fantastic professional and a fantastic lad and I would like to personally thank him for his contribution to the team last season.
"He was crucial to what we achieved and he goes with the very best wishes of everyone at the club.
"I would like to assure our fans that there is a huge amount of work going on behind the scenes. Our aim is to build a competitive squad for the new season and this deal will give us further ability to strengthen the side.''