The two clubs meet tonight in the FA Cup.
Mowbray said: "In adversity, the group of players should be feeding off that and becoming stronger and more unified, and I am sure that's happening at that club.
"The decision for Rafa to take that job was made because he is a top manager who has won European trophies, who has won leagues in just about every country he has been to. He is a good football man. I don't know him well, but I have been in his company and he loves to talk football tactics.
"I have only got respect for Rafa Benitez. It is a tough job, of course, but he seems very professional, long in the tooth regarding his job from the point of view of getting on with his job and trying to win trophies for the club.
"Every football manager at times feels the wrath of the support and you have to be very, very single-minded to sit in a football manager's job in 2013 because of the social media aspect of the world now, everybody can do your job, everybody has got an opinion.
"You have to be single-minded and I think Rafa is showing everybody he is pretty single-minded, getting on with his job, trying to win games. Whenever he loses, it's probably his fault; whenever they win, nothing is said. You do need a thick skin."