Indian Consul-General in Melbourne Anita Nayar said the Premier should have visited Mumbai to send a message that Australians were determined not to be frightened away.
"It would have been great if the premier could have sent that message but I understand that there are constraints," she told reporters here.
"We would have liked him to visit Mumbai. (But) one can never predict what is going to happen. If he had gone and something happened, everybody would say why did you go?" she said.
Brumby had altered his itinerary after Australia's foreign affairs department on Friday issued a travel advisory warning about the possibility of attacks in Mumbai. He will now spend more time in New Delhi after omitting Mumbai from his itinerary for Wednesday and Thursday.
"We need to be guided by advice that comes from DFAT. That advice came in last week and over the weekend. The unanimous view of the Victoria Police, my department head and my office was that I should change my program and I've done that," Brumby said.
"I do that reluctantly but at the end of the day I need to follow that advice," he said.
Brumby is scheduled to attend an AFL Grand Final event and visit a Commonwealth Games site in Delhi on Saturday.
Meanwhile, Deputy Prime Minister Julia Gillard described Brumby's trip as "very important". "Like me, Premier Brumby has been very keen to assure Indian families of international students who visit Melbourne, in particular, that they are safe here, that they are welcome here," she said.
"We've seen (a) disturbing number of incidents involving Indian international students in Melbourne. Any violence against international students is completely unacceptable - it's not the Australian way," she said.
"We want every international student to feel welcome here, to feel safe here, and to have a great experience in this country," she said.