The Twitter outburst followed the emotional pre-match tribute to the 96 Hillsborough victims and an enthralling game which United narrowly won.
The game was only 13 minutes old when a section of United fans tried to provoke their fiercest rivals by chanting "Where's your famous Munich song?"
But the worst episode came after the final whistle when most of the Liverpool fans had left. Two alleged home supporters made aeroplane signals after running towards the corner of the stadium where the United fans remained on police orders. The United contingent responded by singing "Always the victims, never your fault" and "Murderers" in reference to the 1985 Heysel disaster.
"What was done at the end I cannot comment on as I didn't hear or see anything," said Liverpool manager Brendan Rodgers. "There is an intense rivalry here and you don't want that to end because that is all a part of what makes this the biggest game in British football.
"But songs from Liverpool or Manchester supporters, any of us that have any human decency don't like to hear that."
United manager Sir Alex Ferguson was adamant that Halsey, who turned down a Luis Suarez penalty appeal but awarded a contentious one to United after Glen Johnson had tangled with Antonio Valencia, got the key decisions right.
"I thought it was a clear red card," said Ferguson, whose side won at Anfield for the first time since 2007. "I don't think (Shelvey) went for the ball - Jonny Evans went for the ball and got the ball."
- DAILY MAIL