The manager was unhappy that his side were not given a throw-in in the build-up to Clint Dempsey's equaliser and that Wayne Rooney was not given a penalty in the second half
The Red Devils had led through Robin van Persie's header but were pegged back by the American's late strike, meaning their lead over Manchester City at the top of the Premier League has been cut to five points this weekend.
Sir Alex was furious with the performance of one of the referee's assistants, Simon Beck, believing his side should have had a throw-in in the build-up to Dempsey's goal and a penalty for a foul on Wayne Rooney in the second half.
The United boss even recalled how a Beck decision had cost the Red Devils in a key game against Chelsea back in 2010.
"I think we should have had a throw-in down our side of the pitch but that linesman never gave us a thing all day," he told Sky Sports.
"For me, it was a poor performance by him. He never saw the penalty kick for Wayne Rooney and some other decisions too.
"We remember him well from his time at the Chelsea game when Didier Drogba was three yards offside and he gave onside. I think he had a shocking game today and I'm disappointed in his performance, I really am.
"I think he has had a bad game and we never got anything from that side of the pitch. We got a bad break."
The manager did lay some of the blame with his side for losing a late goal and for failing to take opportunities to seal the victory as they were unable to make the most of their threat on the counterattack.
"We were 1-0 up with a minute to go and looking comfortable at that stage," Sir Alex continued.
"Tottenham worked their socks off and you've got to give them credit for that and I suppose you can't deny them their point because they worked ever so hard for it. They just kept pumping the ball into the box and got their rewards for that.
"I think we were getting used to the fact they were hitting long balls into the box and we should have dealt with it better. It's just one of those things; I'll need to see it again.
"I was generally happy with the team's performance. We've worked hard. It was a good quality of game, both sets of players were committed and fought hard for every ball and both teams were aggressive at times.
"For us, with the counterattack we should have killed them off four or five times in the second half. I thought it was the final ball that let us down and we should have been better than that. We had opportunities but if you don't take those chances then 1-0 is not a healthy scoreline in a game of football."
The result cut United's lead to five points in the title race, although Sir Alex didn't feel a draw against Spurs was a poor result.
"Everyone will recognise this was a difficult game," he added. "We've had all our hard games away from home so far so we can be pleased at that part of the season.
"Teams will drop points here, there's no doubt about that. Tottenham are a very good team and they might take points against the teams that matter to us. Manchester City are still to come here."