Border praised Bhajji for his behaviour when he was baited by sections of the SCG crowd.
"I was over that side of the ground and Harbhajan was copping a fair bit of stick from the crowd," Border was quoted as saying by Australian Associated Press (AAP).
"I didn't notice any gestures at all and I thought he handled himself pretty well. "It's not a big deal."
Border, a gentleman cricketer, said it was a shame that a great century by Sachin Tendulkar in his farewell tour of Australia was being overshadowed by "a few bits of silliness in the outfield."
The Herald quoted a spectator saying that Harbhajan had motioned to scratch his armpits and also spat towards the crowd after being abused by spectators.
'Harbhajan is innocent': Meanwhile Indian team management condemned the reports on Harbhajan today and said the impulsive bowler had done nothing wrong.
"I think it is wrong," meadi manager Bimal Soni said.
"Nothing has been done like that. They are making a mountain out of a mole hill. He did nothing.
"These stories I do not believe them and I strongly condemn them."
The Indians fly up to Brisbane today and Soni said the latest controversy wasn't distracting the side before morrow's game two of the best of three finals series at the Gabba.
"We do not talk about it, we only talk about the cricket on the field and we do not want to talk anything about these things," he said.
Hussey plays it with straight bat: Australia's Mike Hussey said he and his team mates knew nothing about the alleged incidents.
"I haven't heard a single thing about it," he told reporters in Sydney.
"I'm not so sure how serious it is."
Hussey also said he believed too much was being made of things away from the game itself.
"I think the Australian and Indian public have had enough of all the controversy," he said.
"We just want to concentrate on the cricket."