After the club’s account asked for recommendations for Sunday’s playlist when United visit Anfield, one fan suggested Frank Sinatra's "Come Fly With Me", Reel 2 Real's "I Like to Move It Move It" and "Always Look On The Bright Side Of Life" by Eric Idle.
The latter two songs have had their lyrics reworked to make derogatory references to the Munich disaster.
A tweet sent from the official Liverpool account replied: "Have you been sneaking a look at the dressing room iPod?"
The tweet has since been hastily deleted and an apology has followed.
A club spokesperson told the Huffington Post: "Liverpool Football Club responded quickly to correct the error of judgement that was made last night on it’s official Twitter account in responding to a distasteful and inappropriate tweet.
“The club took decisive action and the comment was deleted swiftly,” they added.
"We apologise, unreservedly, for any offence that was caused by this mistake."
Liverpool have found themselves embroiled in numerous PR disasters in recent years, most notably concerning the club's ardent support of Luis Suarez.
Then manager Kenny Dalglish and his players famously wore T-shirts declaring their support for the Uruguayan, just a day after he had been suspended for eight matches by the FA for racially abusing United defender Patrice Evra.
Last year, the club's recently-installed director of communications, Jen Chang, was promptly sacked after he was accused of making numerous threats to a Twitter user.
Liverpool-United matches have often been marred by unsavoury chants from both sets of supporters in what is one of the fiercest rivalries in British football.