Liverpool manager Jurgen Klopp felt his side were denied a late match-saving penalty at Old Trafford but accepted that defensive errors had also cost his side.
Marcus Rashford scored twice within 25 minutes before an Eric Bailly own goal gave Liverpool hope midway through the second half.
But for Klopp the key moment arrived nine minutes from time when Sadio Mane raced onto a backheel from Roberto Firmino and fell as he tangled with a challenging Marouane Fellaini.
Jurgen Klopp was left fuming at refereeing decision after Liverpool lost to Manchester United
The Reds manager felt Sadio Mane was fouled by Marouane Fellaini late on at Old Trafford
‘We should have had a penalty around the Fellaini situation with Sadio,’ said Klopp. ‘If the referee (Craig Pawson) or his assistant had seen it, it’s a draw. We would have more points and it would change my life massively.
‘I don’t think anybody could have had a big argument about the draw. But we knew Lukaku can win headers and when he did, we were not there for a second ball. So they scored twice like that. It gave them a big boost.
‘We had good moments chasing the game but it’s all about winning. The two situations that lost us the game had nothing to do with their style our our style.’
Liverpool, who are now five points behind United and can’t feel their top-four status is yet assured, had only two shots on goal at David de Gea in 90 minutes but Klopp said he wasn’t disappointed b that.
Liverpool struggled to break down a stubborn United defensive line at Old Trafford
‘How can I be frustrated if don’t create a lot of chances against a world-class team like United,’ he said. ‘They do what they do at the highest level, to get the third or fourth chance will not happen.
‘Are we under pressure? Yes, but that’s part of our life. We are under pressure whether we are ahead of United or five points behind.’
It was a particularly disappointing afternoon for Liverpool’s player of the season Mohamed Salah who was well-marshalled by Ashley Young and fired over with his only clear opening in injury-time.