With the dust barely settled from captain Inzamam-ul-Haq's ban for bringing the game into disrepute, stand-in skipper Younis caused further chaos on Thursday when he said he did not want to be a "dummy captain."
"Younis's decision to turn down the captaincy shows a lack of attitude and we need to change this attitude if we want to be world-beaters," Woolmer told AFP on Friday.
"I fought for him in the team and helped him fight for his place against all odds, but his decision left me sad and disappointed. It seemed he could not take the pressure of captaincy."
The Pakistan Cricket Board on Thursday named batsman Mohammad Yousuf as captain after Younis dropped his bombshell. The side fly out to India for the Champions Trophy on Saturday.
The 58-year-old Woolmer, a former England batsman who also coached South Africa, said he was now looking to the future.
"I am a firm believer that things happen for the good but we must learn quickly because the people of Pakistan have high expectations of this team and the World Cup is getting nearer," said Woolmer, referring to the four-yearly tournament, taking place in the Caribbean next year.
Pakistan must also mature or else they will face tough times in the post-Inzamam era, Woolmer said.
Master batsman Inzamam is set to return after serving his ban of four one-day internationals for leading his team's refusal to play in the fourth Test against England at The Oval in August.
Inzamam was acquitted by the International Cricket Council on ball-tampering charges, the allegation that led to Pakistan's protest.
But at the age of 36 Inzamam, one of only four players to compile 10,000 one-day runs, is nearing the end of his career.
"Pakistan must learn to live without Inzamam, who has been the binding force in recent years. Inzamam will not always be there, so others will have to show maturity," said Woolmer, who took over as coach in July 2004.
Pakistan are due to leave for Jaipur, India, on Saturday. They open the Champions Trophy with a match against a qualifying team there on Oct 17 before taking on New Zealand (Oct 25) and South Africa (Oct 27), both at Mohali.