Burnley are working to finalise a compensation deal with Bolton for their former boss Owen Coyle who said his goodbyes to club staff on Tuesday.
"We are all grown men, but it was quite emotional when Owen left, he has a big affection for this club," added Kilby.
"I fully expected when he did move it would be upwards, not sideways to a club we are fighting a relegation scrap with. We were surprised.
"But I have been in football long enough to know these things happen and I don't think Owen took this decision lightly.
Steve Davis is the man. We would not need to pay any compensation and I think he would not change our style that much Claretinoz "It was with regret that he went and he did say to me there was only Celtic or Bolton he would leave Burnley for. But it has come at a bad time, that is for sure."
Kilby is now keen to get a new manager in place sooner rather than later.
He added: "We have got to get going. Let's put this behind us and make sure we stay in this Premier League.
"We have to see who is out there. We need to get this one sorted out as soon as we can."
Burnley are due to travel to Bolton for a Premier League fixture on January 26 and Kilby admits relations between the two Lancashire clubs are strained.
"I don't think we (the clubs) are best of pals at the moment," stated Kilby. "It did come at a bad time and it was an unwelcome approach.
"Owen felt Bolton do have a larger player budget than we have and it was his best way of remaining a Premier League manager, working with a budget of that size.
"It's been a trauma for the football club. None of us wanted Owen to go. It was a shock when all this broke."