The five-star hotel, set up in 1905, was seized by terrorists Wednesday night along with a Jewish centre and the Oberoi hotel. The gunmen killed people and then took hostages until commandos neutralised them Saturday.
From the Taj, Deshmukh went over to the Oberoi.
Mumbaikers expressed anger that the chief minister chose to go around the Taj hotel with the film maker, adding to the burden of an already stretched out security personnel.
"Is he taking Ram Gopal Varma so that he (Varma) could make a realistic film one day?" asked Narendra Shinde, an employee of a multinational company.
"This is insensitive (on the part of the chief minister), " said Aruna Anand, a social activist. "Politicians have to exhibit a sense of sensitivity when common people are suffering."
Shiv Sena MP Bharat Kumar Raut said Deshmukh was trying to promote his son and "bring him in front of the camera".
"If they wanted to go to the Taj, they could have gone separately to express solidarity. However, if a film star goes there, it is a practical difficulty for security personnel. There was no necessity to go there. He could have sat at home and expressed solidarity."
Ashok Pandit, also a film maker, called it a "security lapse".
"Even if Riteish is the son of the chief minister and Ram Gopal Varma is a film maker of repute, it is a serious security lapse... The chief minister should resign."
Ram Gopal Varma defended himself.
"I have no intention of making a film ever on this issue. My visit was not to make a film on it.
"Just because it happened to be Riteish, I walked with him. I was not even formally introduced to Vialasrao Deshmukh."