Manchester United boss Jose Mourinho said Liverpool "are not the last wonder of the world that the media like to say they are" after his side held Jurgen Klopp's team to a goalless draw.
In a game of few chances at Anfield, the hosts were largely subdued by United's defensive organisation.
"This is a point that stopped them winning three," said Mourinho.
Klopp was not happy with his side, saying: "We tried to be too quick and lost patience with our passing."
The result leaves Liverpool fourth in the Premier League on 17 points, with United three points adrift in seventh.
Klopp felt his side "wasted a lot of energy" in the first half.
He added: "The second half was better but with a little bit faster legs, we could have created more."
Liverpool forced United goalkeeper David de Gea into two fine second-half stops, the Spaniard diving low to stop Emre Can and saving athletically from Philippe Coutinho.
The visitors had just 35% of possession - their lowest in a Premier League match since Opta began recording the data in 2003-04.
Asked about that statistic, Mourinho told Sky Sports: "That was the game that we played - we don't control the game by having the ball all the time."
He later added: "Two shots on target with 65% of possession. You have to be critical of Liverpool. It is their problem, not our problem."
'People expected us to be really in trouble'
Mourinho has adopted a defensive approach at Anfield before - notably for a 2-0 win with Chelsea in April 2014 that derailed the Reds' title challenge.
This time his side largely suffocated a team that had won their previous four league games.
Describing the draw as a "positive result", the Portuguese said: "The game was difficult for both teams but for longer periods it was more difficult for them than us.
"We controlled the game not just tactically but the emotion of the game. That was probably the quietest Anfield I had and I was expecting it to be the other way.
"The reaction from their crowd was permanent disappointment. People expected us to come here and be really in trouble, which we were not."
United are five points behind leaders Manchester City and Arsenal, and Mourinho feels this will be a significant point as the season progresses.
"Other candidates for the title have easier fixtures at the moment and it is important to keep close to them," he said.
"Our moment to win four or five matches in a row will come and we'll be there."
Midfielder Ander Herrera, who was named man of the match, said: "We did a fantastic job and can be very proud. Every player gave everything and this is the way we have to play big matches."
'That's not the way we want to play'
Klopp said he felt "mixed emotions" after a match he described as "very confusing in many situations" and "too hectic".
He told Sky Sports: "I don't think we played as well as we could have - it's our fault.
"When you defend like Man Utd, that's their style. That's absolutely OK. Players need to be cool and pass the ball to the next player. We were playing risky passes in the first half.
"That's not the way we want to play. We should expect to play better: more patience, more composure."
Liverpool captain Jordan Henderson said: "We defended well but I think we could be a little more decisive in the final third."
Analysis: MOTD2's Martin Keown
United got the point they came for. You have got to give them credit because most teams that go to Anfield just get undone. Usually it is an ordeal but it looked comfortable for them.
It was a really good performance by United - clever in fact.
Liverpool like to win the ball off you high up the pitch, but United denied them that opportunity because they hit it long from every goal-kick instead of trying to play out from the back. How often do you see David de Gea doing that?
United were also using delaying tactics from the off to stop Liverpool finding any of their rhythm. Overall, Jose Mourinho set his side out to frustrate them and they have done exactly that.
United's best player? Ander Herrera, because of his work-rate, the number of times he won the ball, and how close he stuck to Philippe Coutinho throughout. Herrera wasn't even looked on as a starter for United at the beginning of season but is now nailed on in midfield because of the vital job he does for the team.
Liverpool were poor but they looked better when Adam Lallana came on and Roberto Firmino moved from the left to centre-forward. Firmino was making some great runs to stretch United's defence and was far more of a threat than Daniel Sturridge, but it is clear how important Lallana is to Liverpool - he is very clever on the ball.
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