Speaking after his Tigers side defeated Harlequins 19-9 in the LV= Cup on Saturday, Cockerill seemed less than impressed by the way the move Gloucester has been handled.
Gloucester confirmed on Saturday morning they had captured the inside centre, who was later in action for England Saxons against the Irish Wolfhounds, for the 2012-13 season.
Cockerill, while pleased with the performance of some of his youngsters at The Stoop, admits Twelvetrees' exit had left a bitter taste in his mouth.
He said: "Billy's chosen to move on. That's his choice; it's disappointing but that's life.
"I'd rather deal with people face-to-face and be up front. George Skivington is leaving, he came and spoke to me and explained his reasons why. I shook his hand and said 'thanks very much' and wished him all the best.
"That's how I prefer to do business. That's okay. Billy's a young man and he'll learn to do things differently as he matures - as I have."
On the pitch, Leicester got off to the perfect start thanks to Andy Forsyth's converted try in the fifth minute, before Quins replied with a Rory Clegg penalty.
Fly-half Clegg added two more penalties in the second half but while Quins could not fashion a try, the Tigers added two more through Alex Lewington's solo score and number eight Ben Pienaar's well-worked touchdown.
"It was a bit of an odd game really, both sides trying to play and not a huge amount of structure to any of it," said Cockerill.
"I thought [Andy] Forsyth and Dante Mama, who normally plays at Loughborough Students, did really well and [Alex] Lewington's got some pace."
Harlequins have now lost four out of their last six games and head coach John Kingston was far from pleased with his side's performance.
"That was not to the levels that we expect and aspire to," he said. "Yes there's a lot of players out there who are not playing regularly but we're a squad and they will be aspiring to put their hand up. Several of them will be very disappointed because they don't go out there not to perform well.
"Nobody in their right minds is going to expect a team of any sort to carry on with the start we had. We have been winning one losing one in the last few weeks against really very competitive opposition.
"We've got an awful lot ahead of us though and an awful lot of positive things to look forward to."
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