Parikar said this in an interview to New York Times' India blog 'India Ink' which was uploaded Wednesday.
Speaking about the riots of 2002, Parrikar said: "It should not have happened. The administration should have clamped down on any violence. (If I were in his place) I would have ensured (that) but Modi was new to the job as chief minister."
Parrikar, considered close to Modi, also conceded that the Gujarat violence was a blot on Modi's career but said the Gujarat chief minister was not "personally a part of it".
"If he is guilty by connivance he should be punished, but investigations have given him a clean chit. People who oppose him do so because they fear him," Parrikar said.
He said the riots were a product of administrative failure and that everything need not be blamed on Modi alone.
"What happened then was unfortunate, but that does not require his apology. It requires his correction and he has done that.
"There were many reasons why people lost control in 2002 after the bodies (of Hindu pilgrims from an earlier attack) were shown on TV.
"It should not have happened, the administration should have clamped down on any violence," Parrikar said.
The prelude to the interview refers to Parrikar "an affable face of the Hindu right and says that the Indian Institute of Technology (IIT) alumnus "impressed middle class Indians by taking economy class flights, by hailing a taxi himself at the airport, and with clean governance in his state, when political excess and corruption are commonplace".
To a question whether he considers himself a potential candidate for the post of prime minister, Parrikar is quoted as saying: "No, not at all, I am not a candidate."
Parrikar also said that at a time when Manmohan Singh was seen as a lame duck prime minister and the central government was in a "perpetual state of suspension", Modi had emerged as a hope amongst the youth.
"In these circumstances, particularly young people see an alternative model in Modi, and if they want him as prime minister they will have to elect his local representative.
"Also, a substantial number of businessmen are likely to back the BJP this time, and they will also go for Modi.
"I believe a national mood is forming to put the BJP in power and Modi as prime minister," he said.