Liverpool manager Brendan Rodgers insisted the best team lost and blamed mistakes by referee Mark Halsey for contributing to their first defeat to Manchester United at Anfield since 2007.
The Reds dominated for the majority of the match, even after Jonjo Shelvey's 39th-minute red card for a lunge on Jonny Evans, but lost 2-1.
Steven Gerrard's volley gave his side the lead seconds after the interval but Rafael curled in an equaliser before Robin van Persie scored United's first penalty of the season after Glen Johnson was adjudged to have brought down Antonio Valencia.
However, Rodgers took issue with the sending-off, the penalty and Halsey's decision not to award Liverpool a spot-kick when Luis Suarez was felled late in the second half.
"We are bitterly disappointed with the result, I thought the best team lost," he said.
"Of what we could control I thought the players and performance level was outstanding, what we couldn't control were decisions by the referee.
"If Shelvey gets sent off for having both feet off the ground then Evans has to get sent off for that as well if you watch the replays.
"Jonjo is coming in from the side, it is a tackle the player has to go for and one the United player has to go for but the Liverpool player can't get sent off and the United one stay on the field.
"I thought it was very harsh and that was how it was throughout the game as a number of poor decisions went against us.
"The penalty was never a penalty. Johnson has made a fantastic recovery back in and I have no idea why Valencia goes down.
"Up the other end Suarez gets a toe on the ball, gets contact, goes down and doesn't get the penalty.
"It was one of the those days where we never got any decision which could have helped us at all and when you lose a man you need some help."
As Shelvey departed the field he had an angry exchange with United boss Sir Alex Ferguson but Rodgers insists he did not see it.
The midfielder apologised for the tackle.
"I apologise to the fans for getting sent off but no way was I pulling out of that tackle in a game of that importance. I'm sorry," he wrote on Twitter.
Ferguson was bemused by the 20-year-old's reaction.
"He blamed me! But he is young and he will realise the stupidity of it," said the Scot.
"Jonny Evans went for the ball but Shelvey was nowhere near and could have given Jonny Evans a really bad injury - he was very lucky actually."
Ferguson almost agreed with Rodgers in his assessment of the match, although not over the United penalty.
"I thought we were poor. Over the last four years we have allowed the (Anfield) crowd to get at us a little bit," he added.
"They gave fantastic support to their team and they dominated. We played better in the second half but it was against 10 men and Paul Scholes, Michael Carrick and Ryan Giggs' experience got us through.
"No doubts about the penalty though, it was reckless. We haven't played well here for the past four years and we can do better but at least we got a result. It is a turning point for us."
Ferguson was also pleased his side had broken their duck from the spot after three misses - one from Van Persie himself - this season so far.
"It wasn't easy for Robin. He took it well. It was the way he envisaged he would," added the United boss.
Liverpool finished the match with nine men as Martin Kelly hobbled off with a knee problem to give Rodgers more injury problems after defender Daniel Agger sustained possible medial ligament damage and forward Fabio Borini was withdrawn with a swollen ankle.
United looked to have an injury worry of their own when Rio Ferdinand went down in the first half, and although he left Anfield limping, he insisted he was fine.
He said the victory, on an emotionally charged day when Liverpool paid tribute to families of the Hillsborough disaster after the publication of the independent report exonerating fans, more than made up for it.
"It has been four or five years since we got a win here. It was an ugly win, probably our worst performance in that time, but we will take that," he said.
"We didn't get going as an attacking force. We were on the back foot for most of the first half and sometimes it creates its own problems.
"With the occasion and the emotions involved, we just wanted to come here, get the job done and get out with the three points.
"We have done that so we are well pleased. You can get really involved and sometimes the emotion of the occasion can affect you.
"They dealt with it fantastically. You have to pay tribute to that but we won the game - that is all that matters."