The Spanish goalkeeper denied Jurgen Klopp's side the chance to go level with league leader Manchester City, pulling off two magnificent saves from Philippe Coutinho and Emre Can.
Zlatan Ibrahimovic had the visiting side's best chance of the game, but failed to get his header on target from six yards out.
"It's difficult, I have mixed emotions but I'm not happy about the game," Klopp told British broadcaster Sky Sports after the match.
"We started -- how I saw from our body language -- okay and then immediately with their kind of defending, we weren't brave anymore.
"They didn't create chances, they had two maybe in the second half but we had two or three great saves from de Gea. Our performance was not as it should have been but we have a clean sheet, so yippee," he said with more than a hint of sarcasm.
For all the talk of the two sides' contrasting form coming into the match -- Liverpool had enjoyed six consecutive wins -- it was United which started in the ascendancy.
Liverpool's high-tempo gengenpress was efficiently countered with short, sharp passes in midfield, while it was United's own pressing which disrupted the home side's usually fluid attacks.
Marcus Rashford was the beneficiary of the away side's passing, consistently finding space on the right but too often his touch or final pass let his teammates down.
Mourinho and United's early game plan was executed to perfection, stifling Liverpool's creativity and reducing the often raucous Anfield atmosphere to nothing more than a quiet hush.
"I think we controlled the emotion of the game well," Mourinho said. "We could influence the atmosphere in the stadium, always showing their (the fans') disappointment.
"I think they were waiting for an easy match and it wasn't. We had a big chance, I thought Zlatan would score and that's it -- 1-0, goodbye, finished."
And, in typical Mourinho fashion, he couldn't leave without a parting blow to the opposing manager.
"They're not the last wonder of the world like you (the pundits) say they are, but they are a good side."
After half an hour, with neither side able to conjure up a clear-cut chance, it was the tackles in midfield as opposed to goalmouth action that began to get the crowd on its feet.
Ander Herrera against Coutinho became a recurring battle, and Anfield's fabled Kop End led the stadium's uproar when the Spaniard scythed down his Brazilian counterpart on more than one occasion.
It spoke volumes about the lack of entertainment on display that talk on social media was dominated by the stadium's new camera angle.
But while it may not have been easy on the eyes, United deserved credit for restraining a free-flowing team that has created goal-scoring chances at a rate of knots this season.
It took until 10 minutes into the second for either side to create an opening. Paul Pogba's inviting cross into the box found Ibrahimovic unmarked at the far post, but the Swedish international could only direct his header back across goal without troubling Loris Karius.
With that, the game finally burst into life.
Liverpool's passing became quicker and more accurate and began to carve the United defense open. Emre Can was on the receiving end of Coutinho's through ball, but he was denied by the outstretched palm of de Gea.
Again the stadium descended into a quiet murmur but before it fell completely silent, Coutinho unleashed a strike that de Gea acrobatically clawed around the post to lift the 54,000 watching fans back to their feet.
The 'magician' was at the center of everything Liverpool created and a sublime back heel looked to have given compatriot Roberto Firmino one final chance, but Antonio Valencia's blistering pace got him back into position to make a last-ditch tackle.
Despite the best efforts of the home players to finish with a flurry, the game petered out in a manner befitting of the match as a whole.
While disappointed with the overall performance, a diplomatic Klopp was on hand to put the result into perspective in what has been an excellent season thus far.
"We got a point against Manchester United," he said. "I've heard about worse things in the world."