Tottenham and United eventually played out a goalless draw, which left Jones and Co. 10 points adrift of Premier League leaders Chelsea.
But according to Jones, United should have scored at least three goals in the first half, with Tottenham goalkeeper Hugo Lloris getting to half-time with five saves to his name and not being required to add to that tally in the second period.
"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," Jones said.
"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."
Radamel Falcao and Robin van Persie started up front for United at White Hart Lane with the former forcing Lloris into two saves before the break and the latter having one on-target shot thwarted by Tottenham's French goalkeeper.
But although both strikers failed to convert when clear through on goal, Jones refused to blame them for United's failure to triumph.
"I thought Falcao and Robin were terrific today," he said.
"They held the ball up well, they linked up well but it just wasn't our day in front of goal."
Jones added that although fatigue had played a part in United's performance, he and his team-mates could not use it as an excuse because every other Premier League side are in the same position, playing three games in six days across the Christmas and New Year period.
"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 England international said.
"You have to do it, we have done it, and now we look forward to the game against Stoke on Thursday."
