Dimitar Berbatov netted for Spurs in the first-half and it wasn't until injury-time that Carlos Tevez and Michael Dawson contrived to deflect Nani's corner into the Spurs goal.
"It could be massive," United boss Sir Alex Ferguson said. "We don't stop trying and in the last 25 minutes we absolutely battered them. I think we deserved a point.
"The commentator said we've dropped two points but maybe we've gained a point."
United face a Football Association fine for having seven players booked, including Tevez for taking his shirt off while celebrating his part in the leveller.
"For Manchester United it's not right," said Ferguson. "There is something wrong when Manchester United get seven bookings."
Wayne Rooney was booked by Clattenburg for diving after the break - and will miss the Manchester derby next week - but Ferguson felt Tom Huddlestone should have faced the same punishment.
"For me, the first foul the referee should have acted on, Cristiano Ronaldo in the first half, he was hacked down and for me it was a red card," Ferguson said.
"He's kicked him from the back. He spent 30 seconds talking to Jenas. Up to that point, up to half-time, I thought the whole game was looking like it was going to go to pieces as a football spectacle.
"The referee settled down in the second half but nonetheless, for us to get seven bookings something is wrong."
On Rooney's caution, Ferguson added: "If he dived and the referee deems it, he's right to book. But a few minutes later Huddlestone dived, he's already been booked, and he did nothing.
"He told the player to get up on his feet and did nothing about it. You have got to say 'is that fair?'
"Has he been fair to both teams? No he's not, because that was a dive. If Rooney's booked for it, he should be booked for it."
Despite Spurs coming so close to a first win over United since 2001, head coach Juande Ramos remained pleased, particularly with Alan Hutton's debut and Jonathan Woodgate bringing a calmness to the defence.
"When you are playing against a team as good as United, it cannot be two points dropped," said the Spaniard.
"We were close but the game isn't over until the end: we were unlucky but that's the way it is. We've seen that it is an own goal and Michael has said that it is an own goal.
"It was a good game for Hutton, considering he had only trained for two days and he doesn't know his team-mates well. It will see him improve and he will get better as he gets to know his team-mates.
"He is covering one of the weaker areas of the team and we hope with the signings of the players that we will keep improving."
