The tour has been criticised for continuing with the Madeira event after the 52-year-old Zimbabwean, caddying for Scotland's Alastair Forsyth, died of a heart attack during the final round.
The tournament was briefly halted but then resumed after discussions with players and bagmen.
Tour chief executive George O'Grady travelled to this week's Spanish Open in Girona to hold talks with the Caddies Association in a meeting that was also attended by Players Tournament Committee chairman Thomas Bjorn.
"We had a full and frank meeting with (Association) chairman Gerry Byrne and his committee, a meeting which was understandably emotional at times and one during which I apologised to them for the hurt and upset caused by events in Madeira," O'Grady said in a statement on Saturday.
"I completely understand the views of people who say we should not have carried on but it was a terrible situation for anyone to be in and the decision to finish the tournament was not taken lightly, either by myself or by the tournament officials on the ground.
"However, that decision is in the past and the important thing now is we continue to work with Mac's family and friends - as we have done from Sunday - to assist with arrangements surrounding the funeral which will take place in Madeira on Thursday," said O'Grady.
"I have also personally instructed a review of how we deal, operationally, at tournaments with situations such as this so we can ensure the lessons of Madeira are learned."
O'Grady also paid tribute to the dignity shown by twice tour winner Forsyth.
"Throughout this whole process Alastair has behaved like a true gentleman in incredibly challenging circumstances," said the chief executive.
"He accepted our decision to play on in Madeira with grace and dignity and he should command enormous respect for the way he has conducted himself throughout this difficult week."
Byrne said the tour caddies felt it was wrong to continue with the tournament following McGregor's death.
"We went into the meeting unhappy and it was emotional at times but George's humility and honesty in dealing with tough questions was greatly appreciated and it reassured us of the caddies' important position within the tour," added Byrne.
Players and caddies have been encouraged to wear 'Black for Mac' in the first round of the BMW PGA Championship in England on Thursday as a mark of respect.
The Wentworth competition is the tour's flagship event.
- Sports & Recreation
- Alastair Forsyth