Wilkins wonders where the £34m difference in price between the 22-year-old and replacement Tiemoue Bakayoko has come from.
“Chalobah went for £6million. I can't quite see that at £6million. I don't really see the differential between Bakayoko at £40 million and Chalobah at six," Wilkins told the BBC.
“I can't see £34 million difference between the two guys. Chalobah just comes back from the Under-21 European Championships and all of a sudden he is bombed out for £6million.
“£34million comes in and we also sell the best holding midfield player in the country [Nemanja Matic] to one of our biggest rivals. I can't really see how all that happens."
In a statement on the Championship club's website, director of football Phil Giles said: "I'd like to thank Andy for his hard work over the last few years as part of our recruitment team. I believe we have made some good signings in recent transfer windows and Andy has played a strong part in that.
“As always, when a member of staff moves on it provides us with an opportunity to review how we do things and hopefully make the off-pitch team stronger in the process. We will take our time to consider how best to replace Andy. In the meantime, we will share his responsibilities among the remaining staff members and continue as usual.
“On behalf of everyone at the club, I wish Andy well in his new role at Watford."