"Nani looked back and looked at the referee and the referee said 'play on', so what can he do but put the ball in the net?
"You can look at the referee and look at the linesmen and blame them, but the goalkeeper should know better. He's an experienced goalkeeper. I thought he made a mess of it."
The referee's assistant raised his flag after Nani slotted the ball into the net and Clattenburg headed over to discuss the situation.
United skipper Rio Ferdinand also joined them, but it was Tottenham's players who were incensed when Clattenburg allowed the goal to stand.
Numerous Spurs players surrounded both the referee and his assistant Simon Beck, and Luka Modric was eventually booked. The goal came after 84 minutes and Clattenburg was again surrounded by unhappy Tottenham players after the final whistle.
"Clattenburg has not done it on purpose but he has made a mess of it," added Redknapp. "It was as much of a farce as when he disallowed Pedro Mendes' goal a few years ago."
Tottenham should have been awarded a goal in a match at Old Trafford in January 2005 after a long-range shot by Mendes clearly crossed the line before it was scooped out of the net by then United keeper Roy Carroll.
Phelan defends Nani goal
"It's gone now," added Redknapp of the Nani goal when asked whether he would make an official protest.
"In the end Clattenburg will come up with some excuse as to why he didn't see it - he couldn't see, he let play go on - well if he did that he should have been saying to Gomes 'play on, play on'.
"I haven't spoken to the referee, he's not going to change his decision and he's made a mess of it all now anyway. They'll go in and come up with a story that will make it all look right, that's what happens."
The result extended Tottenham's sequences of games against United without victory to 26, with their last win at Old Trafford coming in December 1989.
"It was a a crazy end to the match but it was a decent game of football," said United coach Mike Phelan of Saturday's encounter.
"I guess it is a case of the old adage of playing to the whistle, what else can we ask of our players."
Nemanja Vidic had put United in front with a header from a Nani free-kick in the first half but it was a tight contest.
Rafael van der Vaart hit the post for Spurs as the visiting team played a full part in the game.
"There was very little in the game, it was very evenly balanced," said Redknapp.
Tottenham play Inter Milan in a Champions League tie on Tuesday and could be without the influential Van der Vaart after the Dutchman limped off in the latter stages at Old Trafford.
"It looks like he has done a hamstring," added Redknapp. "He faded a little bit but he hasn't played many full 90-minute games, but he has fantastic ability."
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