United manager Sir Alex Ferguson was left frustrated by the result as his side failed to clinch a win at Tottenham.
With the result, United failed to take advantage of Liverpool and Arsenal both being held to draws earlier on Saturday.
United remain six points behind the Reds at the top of the table, while Chelsea could open up a seven-point gap if they are victorious when they host West Ham on Sunday.
"It is frustrating. I think we dominated the game, but we just needed a little bit of luck," Ferguson said.
"Their goalkeeper made two fantastic saves at the end.
"But you have to be worried about the counter-attack that you could lose it also. (Luka) Modric had a terrific shot near the end that just glanced over that could have embarrassed us."
He added: "Tottenham are not an easy team to play, they are on a high at the moment. Since Harry has come in they have been rejuvenated.
"It’s not the worst result but I would have liked to have got an extra two points as that makes a huge difference.
"After the draws today (Saturday) you hope to take advantage, but now hopefully there will be a draw tomorrow (Sunday) at Chelsea."
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