United have won only one of their last five league games and remain seventh in the league, three points below fourth-place Liverpool and five points off leaders Manchester City.
But having thwarted Liverpool's ambitions of registering a sixth successive win, Mourinho hailed his side's performance.
"We controlled the game, not just tactically, but the emotion of the game," Mourinho told Sky Sports.
"That was probably the quietest Anfield I had and I was expecting it to be the other way. I think was a positive performance.
"The reaction from their crowd was permanent disappointment. People expected us to come here and be really in trouble, which we were not."
He added: "If you analyse the game, you see the reason why we did it, playing (Ashley) Young and (Marouane) Fellaini.
"We had control of the game. There were two amazing saves by David de Gea, it's true, but they were out of context.
"This is a point that stopped them winning three. Other candidates for the title have easier fixtures at the moment and it is important to keep close to them.
"Our opportunity to get five wins in a row will come."
But with his side just two points behind Manchester City and second-place Arsenal in the table, Liverpool manager Jurgen Klopp tried to put things in perspective.
"We didn't play as well as we could have played," said the German, whose side host West Bromwich Albion on Saturday in their next league game.
"We started OK and immediately with their defending we weren't brave anymore. We didn't wait for the right pass.
"They didn't create chances, maybe two in the second half, and De Gea made two or three great saves, but in the end our performance was not what it should be. It is a first clean sheet, so yippee.
"We weren't calm enough. That is not the way we want to play, but I accept it. We got a point. There are worse things in the world."