Gloucester confirmed on Saturday they had captured Twelvetrees who has been in fine form for Leicester this season.
Cockerill admitted he was not impressed with Twelvetrees for the manner in which he engineered his exit from Welford Road.
"Billy's chosen to move on," said Cockerill.
"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," he added.
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