Liverpool outclassed their bitter rivals in a 4-0 win on Tuesday to go top of the Premier League.
United, who missed the chance to move level with fourth-placed Tottenham in the race for a Champions League place, dropped to sixth.
“It’s embarrassing, it’s disappointing, maybe even humiliating,” Rangnick said.
“Especially in the first half, we were just not up to it,” Rangnick also told Sky Sports. “We were nowhere.
“We could have had a back line of six or seven, if you don’t try to win second balls first, not even to speak of first balls… we were second best in all relevant areas of the first half and that is just not good enough.
“They [Liverpool] just showed what kind of calibre they are. We are not up for it. We are not good enough to get points in a game against Liverpool.”
Asked how United can close the gap to Liverpool, he added: “We have to accept they are six years ahead of us now.
“When Jurgen Klopp came they changed at the club and lifted not just the team but the club and city to a new level. That is what needs to happen with us in the next transfer windows.
“There will be a rebuild for sure, that was obvious in the first three or four weeks for me. For us it is extremely embarrassing as a coaching staff to sit here and have a press conference like this. We just have to admit they are better than us.”
Ragnick added: “If you analyse the situation it is not difficult… for me, it is clear there will be six, seven, eight, maybe 10 new players. Before you sign those players you need to be aware how you want to play.”
Mohamed Salah scored twice – ending an eight-game goal drought for club and country – as the hosts once again thrashed United, following their 5-0 win at Old Trafford in October.
United remain three points behind Tottenham, having played one game more. They are level with upcoming opponents Arsenal, in fifth, though the Gunners have played two fewer games.
“The fans don’t deserve us to play this way,” United midfielder Bruno Fernandes told Sky Sports. “They deserve more from us. The way they stay and applaud us, they deserve more. We have to raise our level higher.
“Liverpool is ready for the title, we are not. I don’t need to be here saying about the difference of the level.
“We have to look at ourselves from top to bottom and understand what is going wrong. We are competing until the end. Nobody can put down and think it is over. We have something to fight for.”
During the match, supporters of both clubs joined in a minute’s applause in support of Manchester United’s Cristiano Ronaldo and his family following the death of his baby boy.
The emphatic victory took Jurgen Klopp’s side two points clear of defending champions Manchester City, who can reclaim pole position when they face Brighton on Wednesday.
Heading into the final weeks of the season, the Reds, who have already won the Carabao Cup, remain in the hunt for an unprecedented quadruple for an English club.
This latest display made them the first club to score at least eight Premier League goals against rivals United in a single season.
“I am not here to humiliate opponents – we did what we had to do,” Klopp said. “United are not in a good moment, but for our fans it was a big one and they deserve every bit of joy. Tonight they received a lot of joy.
“I did enjoy tonight. I don’t expect us to be for 95 minutes completely in charge of the game, but for 70 minutes we were in charge and for 20 minutes, while United weren’t in charge, they caused us problems.”
Speaking on Sky Sports, former Liverpool midfielder Graeme Souness said: “This is a fabulous Liverpool team and they are on the brink of true greatness. This is the biggest game in English football and Liverpool were sensational.”