Manchester United boss Sir Alex Ferguson said his side were "lucky" after a 2-1 win at Liverpool.
Ten-man Liverpool took the lead before Rafael Da Silva and Robin van Persie scored to secure a victory for United.
"We were very poor," said Ferguson. "Liverpool dominated the first half and we were lucky.
"In the second half, we had better statistics in terms of possession but we were playing against 10 men so that was disappointing."
Liverpool midfielder Jonjo Shelvey was red-carded for a challenge on Jonny Evans after 39 minutes and Ferguson
"That was silly," added Ferguson. "When he looks at himself he may or may not apologise but it was a reckless challenge.
"It might have done damage and it nearly did because Jonny has got a real bruise above the ankle so he is very lucky."
The match was the first at Anfield which cleared Liverpool fans of blame when 96 of their fans died at the 1989 FA Cup semi-final against Nottingham Forest.
The clubs paid tribute to the victims and their families before the game with Manchester United legend Sir Bobby Charlton presenting flowers to former Liverpool striker Ian Rush.
Opposing captains Steven Gerrard and Ryan Giggs also released 96 red balloons in memory of those who died.
"Liverpool have done a great job in terms of setting the right tone," said Ferguson. "It was not over done - beautiful. It was the right tone and both supporters played their part.
"We'll not stop the rivalry but that goes without saying. What we want is that both sets of supporters don't do the stupid things which over the years have put a stain on both the football clubs.
"Today both sets of supporters honoured each other's clubs."