Matt Ritchie's first goal of the season in the 65th minute was the difference and inflicted a second consecutive away defeat on United as well as handing the Magpies a major survival boost.
Slow start proves costly at tough ground
Although the Red Devils were in control for most of proceedings, Jones admits Newcastle started the strongest: "We didn't show up today, we started slowly and they pressed us and the crowd were on their feet."
Anthony Martial was played through one-on-one with debutant goalkeeper Martin Dúbravka after a defence-splitting pass by Nemanja Matić, but uncharacteristically fluffed his lines.
The Frenchman also had two shots cleared off the line by Dwight Gayle in the second half following a corner while Alexis Sánchez was denied earlier on by a sliding block after rounding Dúbravka.
Jones bemoaned: "We got control midway through the first half and should have scored. We had a few chances cleared off the line, but we weren't at the races, we weren't good enough, it's as simple as that.
"Ultimately we have conceded a sloppy goal and the lads are devastated in the dressing room."
Simply wasn't Manchester United's day
The English centre-back implied that Newcastle were lucky to hold on to their lead until the final whistle, but admitted the Red Devils weren't on their game and three points wouldn't have been deserved.
“In the last 10 or 15 minutes, we had three or four balls cleared off the line," he added. "They were scrapping for their lives and that is the sort of luck they needed and they got it.
"But it wasn’t bad luck today, we just weren’t good enough and I don’t think we deserved to win the game."
"A lot of teams around us keep drawing and losing so there is a lot still to play for," he continued. "It was a disappointing day, but we have to go again. That is all we can do and all we know. We have to improve.”