The northern giants were drawn together for the fourth round of the cup amid heightened tension between the clubs as a result of the Luis Suarez and Patrice Evra racism case that has seen the Uruguayan striker banned for eight matches.
Ayre understands many would have been alarmed at the sides coming together whilst the issue is still hot, but insists the significance of the tie will see the players and clubs make sure it goes ahead without further incident.
He told reporters: “I think there were definitely a few raised eyebrows from everyone after that draw.
“Liverpool - Man United is probably the best fixture in the world and the FA Cup is one of the best competitions in the world, so it’s a great match-up.
“With all that’s gone on, people will talk about it and talk about it but I think the most important thing for us is to make sure that we make it a great day and a great game.
“We need to make sure that we all work together to make sure that everybody concentrates on the excitement of the football and the FA Cup and not on anything else. We are certainly committed to that.”
The Anfield honcho also echoed the importance of anti-racism endeavours in light of the alleged abuse of Tom Adeyemi during Liverpool's third round victory over Oldham on Friday.
“We think it is important, with what went on at the game on Friday and what’s gone on over the last few months, to just reiterate the club’s stance, generally, on racism and on any form of discrimination,” he explained.
“We have been very outspoken and very involved in this type of issue in the past and we have some fantastic people who work every day on those types of programmes.”