United's defensive tactics saw them have just 35 per cent of possession, their lowest total in the Premier League since Opta started collecting data in 2003.
Nevertheless, despite managing just one shot on target and winning only one corner, Mourinho claimed Kop counterpart Jurgen Klopp should be the man under the spotlight.
"Last season United won here. Liverpool had 14 shots on target and Untied had one," said the Portuguese. "How many shots on target did Liverpool have on target today? Two.
"Two shots on target with 65 per cent of possession. You have to be critical of Liverpool. It is their problem, not our problem.
"I think it was a good performance. It was a difficult match for us and for them and I think we controlled the game tactically and emotionally, and it is not easy to do both things here.
"The result I think is acceptable. We wanted more. For long periods in the game we thought that could be possible but we didn't score and, if you don't score, you don't win. But I think it was very positive performance.
"We stopped them playing but they also did very well from 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.
"I think it was their intention to try and control us, which they also did well."