India's victory gave them their first Test series win on Pakistani soil.
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"We depended on our bowlers, particularly Shoaib because he is the fastest bowler in the world. But he has let us down with his performance and attitude," Inzamam said.
Shoaib had fallen during his follow-through on Wednesday's final session with India in a strong position.
He did not take the field on Thursday but batted on Friday, showing no signs of discomfort during a quickfire 28, all in boundaries.
"The way he batted was surprising for me," Inzamam said.
An upset Inzamam said he would ask the Pakistan Cricket Board (PBC) to take action against players who had "dented team spirit".
"Those who don't perform, don't deserve to play," he said.
Former Pakistan captain Rashid Latif had said on television on the first day of the match that Shoaib had called him to complain about lack of support from Inzamam.
"We're looking into this incident. If it's right, we're going to take action," Inzamam said.
The captain also blamed a spate of injuries for his team's defeat.
"Injuries to our key players after the first Test didn't allow us to play a settled bowling combination," he said.
Wicketkeeper Moin Khan, all rounder Abdul Razzaq and seamer Shabbir Ahmed missed the last two matches due to injury. Medium-pacer Umar Gul, the hero of Pakistan's second Test win at Lahore, was out for the deciding Test due to a back strain.
