The 80-year-old -- who on Monday lost his appeal at the Court of Arbitration for Sport (CAS) over a six year ban from football for a two million Swiss franc ($2 million/1.8 million euro) payment to then UEFA boss Michel Platini -- said Infantino had dropped by his house once since he was elected in February and Blatter had raised matters he thought should be dealt with.
"I am definitely not a happy man (with) what happened with FIFA," Blatter told the BBC.
"I have never seen in any company that the new president... was not paying respect to the old president.
"After his election we had a very good contact and he stopped at my house and we had a chat. I told him I have a list of questions that should be solved in Fifa which has not been solved before.
"(Infantino) said 'I will work on that' and he never came back."
Blatter said Infantino, who was UEFA secretary-general under Platini, had not returned his phone calls since that meeting.
"I have asked him, I have sent him a letter and I have his personal number and I was told that it's still correct. Never never an answer - never," said Blatter.
Blatter, who served as FIFA president for 18 years but was subject to withering criticism during his tenure, claims he is too trusting and as a result he and his team never expected the FBI investigation that exposed massive corruption involving senior FIFA members.
"I think people are good, and they are not good," said Blatter.
The Swiss, who served as the faithful secretary-general under his similarly disgraced predecessor as FIFA president the late Joao Havelange, also claims he came perilously close to death late last year.
An unusually dishevelled and unshaven Blatter had alluded to this when he held a press conference last December but he went further with the BBC.
"It was 1 November 2015. I was at the cemetery in my home village -- where we have a family grave. And I was there? very, very weak, I couldn't move," he said.
"They brought me immediately to a hospital in Zurich and they thought I was going to die in the next hours. Seriously.
"It was a lady doctor there and she (asked) me: 'Who should I phone?' And I said: 'No, no, no, I will go home tonight.' And she said: 'Oh no.'
"They brought another doctor and he said: 'OK calm down, calm down.'
"I had time enough in the hospital to think that life is (more) than only football."