While the Red Devils hit back from a goal down on two occasions to claim a share of the spoils at White Hart Lane, stalemate in the capital has left them nine points adrift of table-topping Arsenal.
There are still 25 games to come this season - making 75 points available - but United require a swing of three results in their favour just to draw level with the frontrunners.
Moyes concedes that the reigning champions may have to be perfect from here on in, and is looking for the busy festive period to spark an assault on the top flight crown.
"I think the way we are at the moment, we have to win all of our games," he told MUTV after the Spurs draw.
"I feel we've dropped two points. In normal circumstances, coming to Spurs, and it's been a tough game, you'd feel it was a good result.
"It was a tough game and we had to come from behind twice. Thankfully we did that, but we just couldn't get the third goal.
"I think if you'd said to me before Leverkusen and today that we'd win in Germany and draw here you'd say: 'Hey, they are good results and it's not bad'. The disappointment is going back to last week when we drew at Cardiff.
"I'm concerned we're not as close as we'd like to be [to Arsenal] but it's a long season and hopefully we'll be there or thereabouts. There are a lot of games to go. I think the Premier League is tight and we'll try to stay on the shirt-tails and put ourselves in a good position at the start of next year."
Wayne Rooney was once again United's go-to man against Tottenham, as he bagged a brace, and Moyes admits the England man has returned to his talismanic best after a summer of discontent which saw him angle for a move away from Old Trafford.
The Scot added: "A lot has been said about Wayne. Rightly so because of how well the boy has played with his assists, goals and all-round team play. He deserves people saying how well he's doing.
"Maybe, at times, it was not as good for him last year as he wanted it to be, but the boy turned it around with his hard work and dedication and has got himself in a position where he is playing well, scoring regularly and getting the correct recognition for it."