Gayle in a June 21 diary for a cricket website said: "First and foremost I am very disappointed with the West Indies Cricket Board for not having the guys here in England already and ready to play.
"As the captain I have to say this is disappointing and it is not at all a good start.
"I also have to mention that I was hurt and disappointed that after I was nominated as captain by the selectors, I did not initially get the support of the Board."
Although he remains captain, a WICB statement on Tuesday warned they would "pursue this matter at the end of the tour" and would take "drastic and immediate" action if Gayle stepped out of line again in England.
Gayle, who took over the captaincy from stand-in Test skipper Daren Ganga, appointed after Ramnaresh Sarwan sustained a tour-ending shoulder injury, met with WICB president Kenneth Gordon in London on Monday in a meeting also attended by team manager Michael Findlay.
The WICB statement said: "After lengthy discussions during which Mr. Gayle was made aware of the true circumstances surrounding the matters about which he had unfairly attacked the Board, Mr Gayle was requested to issue a public apology to the WICB for his unfortunate and ill-advised statement.
"He subsequently advised the president and team manager that he was not prepared to apologise.
"In the circumstances, the WICB has issued a very strongly-worded letter of reprimand to Mr Gayle advising him that his conduct is totally unacceptable and that the WICB will pursue this matter at the end of the tour.
"The WICB is hopeful that notwithstanding his unwillingness to apologise, Mr Gayle will understand the seriousness of his actions and avoid any further statements or behaviour that will force the WICB to take drastic and immediate action against him."
West Indies, who recently lost their four-match Test series against England 3-0, face England in back-to-back Twenty20 matches at The Oval starting on Thursday before taking on their hosts in three one-day internationals.
West Indies lost a Twenty20 match against Derbyshire by 51 runs on Sunday.