Siraj and Bumrah were racially abused by the crowd at the Sydney Cricket Ground.
According to Ojha, the Board of Control for Cricket in India (BCCI) should take up the issue with the International Cricket Council (ICC) and make sure a strong message is sent to Cricket Australia (CA).
"Now, Ajinkya Rahane, the coach and the management and the BCCI have to take it up seriously. This shouldn't affect the game. Cricket has to be played the way it has to be played. But after the game is done, we should take it till this has been addressed in the strictest way. They should make sure that a very strong message should go to Cricket Australia and ICC should back it," Ojha told Sports Today.
"What happened during the monkey gate? Cricket Australia raised the issue and the ICC stepped in. I think players should inform the management and the BCCI has to take it up, saying that in a country like Australia, people getting drunk and doing this, it is nonsense. When we play in India, we manage to make sure nobody is racially abused. They have to be strict on this," he added.
There were dramatic scenes outside the Indian dressing rooms after stumps on Day 3, with ICC and stadium security officers locked in long discussions with Bumrah, Siraj and members of team management.
Senior Indian players including skipper Ajinkya Rahane also had a word with the match officials and security officials at the end of play.
According to ICC's anti-discrimination policy, the apex body expects its members to impose sanctions on spectators found guilty of racial abuse.
"It requires ICC Members to impose punishments on spectators found guilty of discrimination, which may include ejection from the venue or a ban of a specified period from attending venues within the Member's jurisdiction to watch cricket, and to deliver preventative measures at International Matches."