Hamilton has brought his pet dog Roscoe to both the grands prix in Europe this year, taking it for walks in the paddock and tweeting pictures of it in the Mercedes garage. However, Watson believes such behaviour is symptomatic of Hamilton's loss of focus since he joined his new team Mercedes.
"There is no place for a dog in the F1 paddock," Watson told the Daily Express. "For one thing, it is not fair on the animal. It might be in luxurious surroundings, but an engine firing up is like a firecracker or bomb going off for a dog. It's not right.
"It just shows that Mercedes are bending over too far to please Lewis. There is absolutely no way McLaren would have allowed it. Lewis wanted more freedom from McLaren and he has got that, but it can go too far the other way."
Watson said Mercedes ought to help Hamilton focus on the racing and block out other distractions.
"Lewis has to decide if he wants to be an F1 driver or a hip-hop star," he added. "At the end of the day, you have got to respect the job that you are doing. He went to Mercedes with the reputation of being the man who would get the job done. Niki Lauda took the credit for getting him in there.
"Niki is an experienced former driver who won three world titles. You don't do that just being quite nice and he should be there trying to help Lewis work his way through the problems and point out what Mercedes expect from him.
"If your life was on the line and it was all down to one lap, you would back Lewis over Nico every time. But it is just not happening for him at the minute and he needs to start working out why."