Coyle had steered the club to promotion from the Championship the previous season before the Clarets made a promising start to life in the Premier League.
However, he found the opportunity to take charge of Bolton, where he had spent time as a player, too tempting to resist following the dismissal of Gary Megson midway through the campaign.
Incoming manager Brian Laws had little time to assess his squad before the transfer window closed and Burnley, who were already slipping down the table, eventually suffered relegation.
Burnley failed to make the Championship play-offs under Eddie Howe last season and Kilby concedes they are still getting to grips with Coyle's exit.
"I don't think people realise the trauma that the complete disappearance of your manager and the coaching staff can leave behind," Kilby said in the Daily Mirror.
"In one week in the middle of your inaugural Premier League season and right in the middle of the transfer window.
"That was tremendously difficult for the club to deal with and we're still recovering from that now."
Source: Team Talk
Source: Team Talk