There was nothing to separate the arch rivals at Anfield as they played out just the second goalless draw in this fixture's Premier League history.
United returned home happy with a point, having come up against a Liverpool side in stellar form, but Mourinho was criticised for the style of play adopted which saw the Red Devils record their lowest possession count in more than a decade.
Karius took it as a tribute to his side's attacking qualities, telling reporters: "We knew we had to be patient because it's going to be tough.
"United maybe waited for the one chance to get a goal, as obviously their priority was to stop our play, our attacks. They know we're a really strong team, so that's a compliment for us. Second half, we managed better to get through, but United defended well with David de Gea making top saves."
The point was enough to lift Liverpool back into the top four ahead of their home meeting with West Bromwich Albion next weekend.