United dominated the first half at White Hart Lane, but a combination of a lack of composure in front of goal and fine saves from Hugo Lloris ensured they were unable to find the net.
Tottenham raised their game after the break, but neither side could find the elusive opening goal and claimed a point apiece from their final Premier League game of the year.
United are now unbeaten in nine games and will head into their New Year's Day clash at Stoke City in third place, but manager Van Gaal was left to ponder what might have been.
He said: "You need a little fortune, because Tottenham could also score in the second half.
"When you play against a top-six club at White Hart Lane and you create six to eight chances, and open chances, then you have to finish that. But you don't reward yourself, then normally the opponent win.
"You could see in the second half it was not football anymore, it was a struggle for life. Tottenham won the second balls and that's why they were more dominating than Manchester in the second half.
"They create three chances, but we also created three chances; [Juan] Mata, [Robin] Van Persie and [Radamel] Falcao."
Van Gaal believes United's inability to beat Aston Villa in their previous away game and Tottenham will make it very difficult for them to win the title.
He added: "I said in the dressing room, when you cannot win such type of matches that you are the better team, against Aston Villa and now against Tottenham, then it's very difficult to be the champion at the end of the season."
