The criticism of Bari was in an ICC letter to the Pakistan official that had "unfortunately" found its way to the press due to a lack of clear instructions by him to prevent its publication, the council said on Thursday.
Bari, a former Pakistan captain, had hit out at two controversial decisions made by Shepherd in Pakistan's 17-run defeat against Australia in the tri-series final at Amstelveen, Holland late last month.
ICC corporate affairs general manager Brendon McClements said the council regretted that a letter from the ICC in response to Bari's complaints had been made public.
"I understand that this has now placed you in a difficult position, a situation that all of us would prefer not to have occurred," ICC said in another letter to Bari.
"My comments were sought on how to address the potential impact on Mr. Shepherd in particular and the Elite Panel of umpires in general that your public criticism of the umpire would cause if it went unchallenged.
"The comment was made within my team that the most open and transparent way to deal with this issue would be to make public the fact that this letter has been sent.
"Unfortunately, I was not clear in the instructions I issued within my department and as a result of this lack of clarity, the actual contents of the letter were placed into the public domain," McClements said.
"I should have been more explicit in my instructions within my department so that this unfortunate situation would have been avoided," he said.
Bari had called for the 63-year old Shepherd to retire after the veteran umpire adjudged captain Inzamam-ul-Haq and Yousuf Youhana out which derailed Pakistan's victory march.
But the ICC, game's governing body, took a strong note of the criticism and warned Bari over his future conduct.
ICC chief executive Malcolm Speed warned Bari in the original letter which ended up in the press that his comments were "inflammatory" and were "out of order."
"I will ask the ICC Board to include selectors as a specific category of officials so that you and other selectors can be in no doubt about where you stand," said Speed in his letter.
Pakistan Cricket Board (PCB) kept away from the controversy, saying it would not reprimand Bari over his comments as he works in an honorary capacity.