Marcus Rashford scored twice on his recall to the starting XI to give Mourinho’s side the points despite a largely defensive display in which they had just 32% of possession and two shots on target.
“It was a complete performance by us with two different halves,” Mourinho said. “If people don’t think we deserved it, I don’t care.
“I am a bit tired, we have a match on Tuesday. I don’t care what people say. The boys are happy, I’m happy.”
The win meant Mourinho’s side narrowed the gap on runaway leaders Manchester City to 13 points – at least until City play at Stoke on Monday – but, more pertinently, they are now five points clear of the third-placed Merseysiders.
Rashford, making his first league start since 26 December, will rightly grab the headlines but Romelu Lukaku was instrumental in both goals, and Liverpool simply could not deal with his physical power in the first half.
First, the Belgium striker’s header from David de Gea’s clearance found Rashford charging into the visitors’ box, and he cut inside Trent Alexander-Arnold before firing into the bottom corner.
For United’s second goal, Lukaku held up the ball from another goal-kick before feeding Juan Mata and, although he could not get a shot away, the ball fell for Rashford to score via a slight deflection from Alexander-Arnold.
At that stage Liverpool were second best in every area of the pitch and could have fallen further behind when Mata volleyed acrobatically wide from an Alexis Sanchez cross.
Jurgen Klopp’s side improved dramatically after the break and, with United defending deep, the visitors cranked up the pressure without ever really opening up their hosts.
It took an own goal for the Reds to reduce the deficit when Eric Bailly turned Sadio Mane’s cross past De Gea while attempting to clear at the near post.
That gave Liverpool’s travelling fans hope but their side could not fashion any further clear chances, even in six often chaotic minutes of stoppage time.
United survived to clinch victory in the first of three games here in the next seven days that will shape their season.
Next up are Sevilla on Tuesday, with a place in the last eight of the Champions League at stake, before they face Brighton in the FA Cup quarter-finals next Saturday.
‘The human brain is a complex thing’
It is the perfect start to a pivotal week for United as Mourinho’s side chase more silverware and a guaranteed ticket to next season’s Champions League.
His side barely made it out of their own half in the second 45 minutes but De Gea only had two routine saves to make as Liverpool failed to break down the organised ranks.
“You can be in control without having the ball, you can be in trouble when you have the ball,” Mourinho said.
“It is an important win. The three games in the league, the Champions League and the FA Cup are independent events, with no relation to the next match.
“But the human brain is a complex thing. A defeat leaves a bit of damage and victory makes happiness even if you are fatigued.”
Russia-bound Rashford returns to run riot
The arrival of Sanchez from Arsenal in January has had ramifications for several United players, including Rashford, who had played fewer than 100 minutes in the league as a substitute in 2018 before Saturday.
Rashford has had to wait for his chance but, in front of watching England manager Gareth Southgate, he did not waste it. After the match Mourinho suggested that Southgate has already said that Rashford’s place at the World Cup is safe.
“I spoke with Gareth Southgate a few weeks ago and Gareth told me it doesn’t matter if he plays or he doesn’t play,” Mourinho said.
“He trusts the kid and the kid goes to the World Cup, so he didn’t need to impress Gareth, Gareth knows what he is and Gareth knows that he can give us things at the World Cup.”
With Paul Pogba injured, Sanchez moved inside to play in the hole behind Lukaku, with Rashford and Mata coming back into the team on the left and right.
And while Sanchez again failed to impress, Rashford showed his lack of minutes has not affected his sharpness or his appetite in front of goal.
The 20-year-old now has 12 goals in all competitions this season, making this his most prolific campaign yet, and he received a standing ovation when he was replaced – although some fans were not happy he was withdrawn.
“The fans they can do what they want, I’m not upset at all with that reaction,” Mourinho said.