The Red Devils had just 35% possession during the match as they managed to successfully stifle their arch rivals to a goalless draw on Merseyside.
Jurgen Klopp's side registered just three shots on target, while United could only muster one across 90 minutes.
Mourinho's side faced criticism for their approach, but the Portuguese has taken a subtle dig at Liverpool by claiming that they should be praised for their defensive performance.
"We didn't get the result we wanted. We wanted to win and just got a point so we were not 100% successful," Mourinho told reporters.
"I think you are very unfair with Liverpool because they had a fantastic defensive performance. For the first time they played with two central midfielders, first time they played [Jordan] Henderson and [Emre] Can together, for the first time they took a striker off to play another midfielder.
"That 0-0 result was because two teams were really good defensively."
Meanwhile, United are preparing for Thursday night's Europa League Group A game against Fenerbahce at Old Trafford.