He accused Sinha of acting in tandem with senior Congress leader and former finance minister P Chidambaram, forgetting the harsh words the two had used for each other.
At a book release function, Jaitley refrained from taking Sinha's name but said he does not have the luxury as yet of being a former finance minister nor does he have the luxury of being a former finance minister who has turned a columnist.
The first reference was for Sinha and the second one for Chidambaram, who rode on the BJP leader's criticism to assail Jaitley and the government's handling of the economy post demonetisation and transitionary impact caused by GST.
Being a former finance minister "I can conveniently forget a policy paralysis (during UPA-II). I can conveniently forget the 15 per cent NPAs of 1998 and 2002 (during Sinha's term as finance minister). I can conveniently forget the $4 billion reserve left in 1991 and I can switch over and change the narrative," he said.
"Acting in tandem itself wont change the facts," he said as he took a jibe at Sinha for seeking a job by making those comments.
"Probably, a more appropriate title for the book would have been 'India @70, Modi @3.5 and a job applicant @ 80," he said, at the release of book titled 'India @70 Modi @3.5'.
Sinha, 84, in a newspaper article headlined "I need to speak up now" criticised Jaitley over the "mess the finance minister has made of the economy" and went on to slam the government over decisions like note ban and the GST, the new universal tax regime.
"The prime minister claims that he has seen poverty from close quarters. His finance minister is working over-time to make sure that all Indians also see it from equally close quarters," Sinha had written.
Jaitley recalled the advice given to him by senior L K Advani when he spoke in Parliament in 1999 on the Bofors issue, of not making personal comments while speaking on issues.
He said he had some very distinguished predecessors including a former President (Pranab Mukherjee) and a former Prime Minister (Manmohan Singh) and the other predecessors have "decided to act in concert."
"Because speaking on persons and then bypassing the issues is something which is very easily done," he said.
The Finance Minister, who is facing criticism for overseeing economy to slip to its slowest pace of growth in three years, said he has done a little research to pull out what Sinha and Chidambaram had to say about each other in the past.
"One said of the other: 'Chidambaram will have to be born again to match my record as finance minister'. He then linked Finance Minister Chidambaram to an incompetent doctor for failing to curb India's alarming fiscal deficit. And then went on and said 'I accuse him of running the economy down to the ground," he said in apparent reference to comments made by Sinha.
The former finance minister, he said, had accused Chidambaram of being "the most conceited person" who bugged his phones.
"'Today with the complete responsibility I want to say when I raised the issue of Aircel-Maxis, Chidambaram ordered my phones to be bugged'," Jaitley quoted him as saying.
Not to be left behind, Chidambaram called Sinha's tenure during the Vajpayee government as the "worst years since liberalisation".
"The other one was not to be left behind. And he said 'I thought Shri Sinha would be happy to remain a distant memory for the people of India. However, since he seems determined to stay relevant in his party, I am obliged to recall his record during his four years as finance minister. I may point out the 2000-2001 and 2002-2003 were the worst years since liberalisation in terms of growth and Prime Minister Vajpayee had then to force him out and replace him'," he said.