The Red Devils entered a heavyweight encounter against arch-rivals knowing that their second-place standing in the Premier League table was under threat.
A Marcus Rashford double, however, moved them five points clear of the chasing pack and strengthened their position behind Manchester City.
An own goal from Eric Bailly provided the only blot on United’s copybook against Liverpool, with Mourinho – who has faced plenty of criticism for adopting a defensive mindset this season – of the opinion that his side were always in control of the game and worthy winners.
He told Sky Sports: "We can split the halves - United first half and Liverpool second but in my opinion our first half was a half with goals and danger.
"In the second half - in my opinion, and probably the people in the studio have a different opinion - was Liverpool controlling with the ball and United controlling without the ball.
"Our team was always in control. Even in set-pieces, corners, dangerous situations we were in control so I think we deserved it.
"Against Liverpool if you play bad when you have the ball you can be in trouble. In the second half it was not our intention - I cannot say this was the plan. Liverpool pushed us into a defensive situation but we kept control. It was a complete performance by us with two different halves.
"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."
United cannot revel in victory over Liverpool for long as their next outing is just as important.
That contest is currently locked at 0-0, so Mourinho will need to encourage another impressive performance from his players if they are to prolong their European adventure.