"We depended a lot on Shoaib because he is one of the fastest bowlers in the world, but he let us down badly," a visibly agitated Inzamam said.
Inzamam's outburst came after India completed a historic maiden series victory on Pakistan soil after crushing their archrivals in the decisive third Test by an innings and 131 runs in Rawalpindi.
The Pakistan captain was particularly annoyed at Akhtar for declining to take the field on Thursday when India were batting after complaining of a side strain.
Akhtar, however, batted on Friday, smashing 28 off 14 deliveries with four boundaries and two sixes.
"I can't say if the side strain had affected Shoaib's bowling, but it is difficult to bat like this when one is injured," Inzamam said.
"Everyone has seen his attitude, I don't have to comment on it. But only those who are interested in playing for Pakistan should be picked.
"I have heard that Shoaib told someone that he did not want to bowl because I was not giving him the field he wanted.
"If what he said is true, I will insist that action be taken against him because comments like this have a negative impact on the whole team. You are not expected to behave like this in professional cricket."
India won the first Test at Multan by an innings and 52 runs, before Pakistan drew level at Lahore with a nine-wicket triumph.
Inzamam said the poor form of Akhtar, who managed just seven wickets in the entire series at an average of 42, and injuries to key bowlers was the major reason for the defeat.
"I expected a lot from the bowlers, but they allowed India to post big scores in the first and third Tests which we lost badly," he said.
"We had one good Test in Lahore, but then we lost the main bowler in that match, Umar Gul, due to a back injury.
"We also did not have the services of Abdul Razzaq and Shabbir Ahmed for two Tests. These injuries cost us dearly but I am not offering any excuses. We lost because India played better cricket than us and we did not play to our potential."
Inzamam, meanwhile found an unexpected ally in his Indian counterpart Sourav Ganguly, who said the young Pakistan team needed time to become a world-class unit.
"Pakistan have in the last year lost veterans like Saeed Anwar, Waqar Younis and Wasim Akram," said Ganguly.
"It is not easy to replace players of that stature. When a team loses, especially in the subcontinent, a lot of criticism is aired.
"But this Pakistani team is a young one. Give it time and it will improve. I reckon Pakistan will once again become a good side."