Director of football Steve Coppell insists Crawley went about recruiting Bury manager Richie Barker in the "proper way".
Barker signed a two-year contract at the Broadfield Stadium on Tuesday to end Crawley's search to replace Sean O'Driscoll, who departed for Nottingham Forest last month.
Barker took over at Bury in April 2011, helping the club to promotion from League Two, and he consolidated the Shakers' League One status with a 14th-place finish last season.
The Greater Manchester club have agreed to a compensation package for Barker but Coppell admits Bury are not happy to be losing the services of the 37-year-old.
"Things have to be done in a proper way. Bury aren't happy to be losing their manager," he told the club's official website.
"Richie's family live not far from here so they (Bury) accept it's being done for proper reasons. We've done everything by the board and thankfully we have got our man."