However, Liverpool-born Moore admitted that some issues are out of the club's control.
UEFA have made available only 16,626 tickets to each club - out of a total capacity of 70,000 at the Olimpiyskiy National Sports Complex in Kiev.
Out of the tickets allocated to supporters, only 63% were available to the general fanbase.
In addition to the low ticket allowance, fans that are travelling to Ukraine have found it difficult to source hotels and flights for a reasonable price, with many vendors increasing their prices.
Many supporters have been left without travel and accommodation options, despite receiving tickets via the ballot. Moore admitted these problems are far from ideal, but said some issues are beyond the club's control.
"As a club, we are acutely aware of the issues that our supporters are facing in terms of obtaining tickets, arranging travel, and organising accommodation for the forthcoming Champions League Final in Kiev," Moore told the Liverpool Echo.
"It is for that reason that we have worked exhaustively to try to alleviate some of these difficulties, whether that be by collaborating with partners, liaising with the relevant authorities in Kiev or by asking our own staff to go the extra mile – something that they have done willingly and without hesitation.
"Some of the issues are, unfortunately, beyond our control. Logistically, the challenges of this event are there for all to see and whichever clubs reached the final would have faced the same problems. As it is, we are doing our level best in exacting circumstances to make the best of the situation on behalf of supporters.
"Nevertheless, we will always strive to do better for our supporters and will always listen to their concerns. If there is one thing that this Champions League campaign has underlined it is that anything is possible when there is unity between players, club and fans and that remains a fundamental objective for everyone at Liverpool FC."
Liverpool play Real Madrid in the Champions League final at the Kiev Olympic Stadium on Saturday, May 26.