Alex Ferguson has said it will always be important to him for Manchester United to beat Liverpool, no matter where their northwest rivals stand in the Premier League.
Leaders United overcame a late Liverpool rally to claim a 2-1 win at Old Trafford.
The victory saw United go a huge 24 points in front of Liverpool, who remained eighth. But Ferguson said: "Winning these games is important. It doesn't matter what position we are in the league.
"Manchester United and Liverpool games are a fantastic challenge, and those three points are hopefully very important for us."
Despite a few late scares with Fabio Borini and Daniel Sturridge going close for Liverpool, United clung on for victory.
"Until the second goal we were magnificent. It was as good a performance as we've had for a long time," said Ferguson. "But when they got the goal they were inspired and it was hard work after that."
Liverpool manager Brendan Rodgers believes his side's second-half display proves they are starting to close the gap.
"I think this performance gives us great hope," Rodgers said. "We are 24 points behind Manchester United, but we are not 24 points behind in quality.
"Once we close the gap in terms of the squad depth, I have great faith that we will be able to challenge."