Writing on Cricinfo Web site (www.cricinfo.com), Shaharyar Khan wrote that Inzamam would go into a "brooding silence" for days after disagreements with Briton Woolmer.
Khan also revealed that Woolmer offered to quit last year over a ball-tampering scandal in England which led to the only forfeiture of a test match in cricket history.
The coach was murdered in Kingston last Sunday less than 24 hours after Pakistan's shock World Cup elimination from the World Cup by Ireland.
Jamaican police said on Sunday they were still sifting through clues as to the identity of his murderer or killers.
Shaharyar wrote of Woolmer's many difficulties in serving as Pakistan coach from 2004 in a long appreciation of the 58-year-old coach for the Web site.
He said one had been problems with senior members of the board who, Woolmer felt, undermined his authority.
"The second obstacle that Bob faced was control of the team. Here he found that the captain's spiritual hold on the team prevented his holding full sway with the players, especially the senior members.
'CRICKETING DIFFERENCES'
"Bob had some cricketing differences with Inzamam-ul-Haq but these were addressed through dialogue and mutual understanding, even though for days the captain would go into a brooding silence
"The more serious issue was that Inzamam was not only the cricketing leader but the spiritual talisman of the team who expected -- and was mostly given -- total obeisance by his team mates."
Khan said Woolmer had nearly followed him in resigning following the forfeiture of the fourth Oval test in England last year when Pakistan were accused of ball-tampering. They were later cleared.
"On October 6, the day I resigned, Bob came to me with red eyes and said that he would also resign.
"I persuaded him not to do so, assuring him that I knew the new chairman would give him his full backing.
"I told Bob that the patron greatly appreciated his contribution in raising the team's performance and had on several occasions expressed this appreciation and had reiterated the need to support the coach."
Khan paid tribute to Woolmer's skills of diplomacy and his ability to foster team work among players who were a disunited force when he took over.
"Two days before leaving for the Caribbean, Bob came to see me saying he would be prepared to serve Pakistan even after the World Cup but the continuous sniping and harassment from PCB's senior elements would have to stop.
"He felt that it had been hugely disruptive to preparations and team morale. I again advised Bob to place his trust in the new chairman before making his decision."
Khan said he regarded Woolmer's death as a "national and personal tragedy".
(Writing by Jon Bramley in Barbados)