The Red Devils missed a number of good opportunities to take all three points from White Hart Lane, passing up the chance to close up on the Premier League's top two after both Chelsea and Manchester City also drew later in the day.
Juan Mata saw a deflected free-kick hit the post while Radamel Falcao, Robin van Persie, Ashley Young and Wayne Rooney all came close, with Tottenham goalkeeper Hugo Lloris in fine form in the opening 45 minutes.
But the hosts came back into the contest after the break as United seemed to tire, with manager Louis van Gaal naming the same side that started the 3-1 win over Newcastle less than two days previous.
Jones played the whole 90 minutes in both games and the England defender insisted it was an unfortunate day at the office that cost United the three points, rather than a lack of energy.
"I think fatigue is always going to kick in with two games in three days but it's the same for every club in the Premier League," the 22-year-old told MUTV.
"You have to do it, we have done it, and now we look forward to the game against Stoke on Thursday
We created numerous chances in the first half and perhaps should have been three or four nil up at half-time, but it wasn't to be.
"In the second half they came out and pushed us to the end
We knew that would happen, but we stayed resilient and we kept a clean sheet.
"It's always nice to come away with a clean sheet but ultimately the lads are disappointed not to have taken all three points
I thought Falcao and Robin were terrific today
They held the ball up well, they linked up well but it just wasn't our day in front of goal."
Tottenham were the side pushing for a winner as the game progressed, with midfielder Ryan Mason guilty of missing the best chance to wrap up the win for the hosts.
But United could have been out of sight by then had it not been for the heroics of Lloris, who praised the fitness of his team-mates.
"We finished the game stronger than United physically and we were close to getting a chance to score," the Frenchman told Tottenham's official website.
"I think overall the draw was fair because in the first half they had some good chances
But we were strong and after that, we know we have the quality to score a goal at any moment.
"Manchester United have a lot of world-class players and they showed it
They could be a challenger for the title as well, so it's good for us not to concede three points to them and the draw helps us to stay close to the third position."
Source : PA
Source: PA