United produced a performance typical of a Mourinho-led team on the road, stifling its in-form opponent to earn a share of the spoils on Tuesday (AEDT).
Liverpool, which had won four successive Premier League fixtures heading into the contest, was frustrated by United from the opening whistle, though the host was twice denied by the brilliance of goalkeeper David de Gea in the second half.
United ended the match with just 35 per cent possession - its lowest since Opta began recording data in 2003-2004 - but Mourinho disputed the stat post-game as he shifted the focus on Liverpool.
"I've just been told it was not 35 per cent. It was 42 per cent. That is from our guy," Mourinho told reporters as he returned to the news conference.
Earlier, the Portuguese insisted: "Last season United won here and Liverpool had 14 shots and United had one. Today Liverpool two shots? With 65 per cent of possession you have to be critical of Liverpool not us. That is their problem not our problem.
"I think the team was perfect. Even the goalkeeper was on holiday for 90 minutes but he had two big saves to do and he did."
The Manchester United boss then went on to say Liverpool was being overhyped by the media.
"We knew it would be very difficult for them to score a goal and we thought we'd score the goal to win the match. We tried to start strong in both halves but they are a good team. But they're not the next wonder of the world like you try to say they are."
Mourinho, whose United remains three points behind Liverpool and five adrift of Manchester City and Arsenal in seventh, said: "We stopped them to play, but they also did very well by the defensive point of view. They played [Emre] Can and [Jordan] Henderson for some reason, and they did that for 90 minutes, so they normally project more players in attack.
"They were very cautious, they kept always Can and Henderson in position, they had only one player behind the three more offensive players, so I think it was that intention to try and control us, which they also did well.
"I think it was a good performance, difficult match for us and for them and I think we controlled the game tactically and we controlled the game emotionally, and it's not easy to do both things in here.
"The result I think is acceptable, we wanted more for long periods in the game we thought that we could be positive but we didn't score and we don't score we don't win, but I think a very positive performance."