Worrall completed his move to the New York Stadium for an undisclosed fee on Thursday but Day has made it clear that Shakers manager Kevin Blackwell was keen to retain the 23-year-old for the forthcoming League Two campaign.
As such, the recently installed Gigg Lane chief went on to offer assurances to fans on the club's official website.
Day's statement read: "As the chairman of this club, I think it's essential that the fans have access to all information and reasoning behind the decisions we as a board have to make.
"I was approached by the agent of David Worrall and it was made clear to me that the player no longer wished to play for the club. I stated that he was part of the manager's plans and the new board wanted him to stay.
"He made it clear that if we did not allow him to move, then the player would exercise his rights to move as soon as he was contractually entitled.
"As a result we had to make a decision based on the best interests of Bury Football Club. The player was therefore sold.
"I wanted to make it clear to any fan that feels we are selling our best players that this is definitely not the case and the next few weeks will demonstrate the quality of players we have targeted to bring into this club.
"We do not want to keep any player that is not prepared to give this club 100 per cent. We will update you on all new signings as soon as they have been secured."