Taylor, 28, was dumped as Test captain last week and replaced by Brendon McCullum, who will take charge for all three forms of the international game starting with the tour of South Africa.
Moller believes it was the correct decision but added: "Yes, the ball's been dropped, absolutely. Could we have done things better? Absolutely. Are we going to learn from those mistakes? Well, we hope so."
Moller's statement also contained an apology to Taylor, which was accepted by the top-order batsman.
Taylor wrote on Twitter: "I appreciate the apology from NZC today. Keen to put it behind me and looking forward to getting back with the team soon."
Moller also revealed there had been some "additional material" brought to NZC's attention over the Taylor situation.
He would not go into further details, adding: "We are on the case, but I'm not going to put an arbitrary deadline (on it).
"We will move forward as quickly as we can but we do these things - although the events of the last week may not evidence this - we'd like to think we do these things in a considered, sensible and well thought out manner."