Spurs were perhaps unfortunate to be trailing following Nemanja Vidic's 31st-minute header following an end-to-end first half and saw their hopes of a late leveller dashed when the Portuguese winger netted in controversial circumstances five minutes from time.
Nani had a penalty appeal turned down after bursting into the Tottenham box and was seen handling the ball while on lying on the turf.
But while goalkeeper Heurelho Gomes lined up what he believed to be a free-kick, the United man stole in front of the Brazilian and prodded into a vacant net.
A lengthy discussion between linesman Simon Beck and ref Mark Clattenburg followed, with the official later awarding the goal having never blown for a free-kick.
A seething Redknapp said: "What a farcical way to finish a game. It's a handball, he's deliberately handled it and it should have been a booking.
"Everyone has seen him do it so we think it's a free-kick, it's just the referee that doesn't see it.
"Everyone saw him do it so it's a free-kick. You can't lie on the floor and pull the ball back just because you've got the hump because you didn't get a penalty.
"It was a scandalous decision and the referee has made a mess of it all."
Clattenburg was famously the referee who refused to allow Pedro Mendes' 'goal' against United in 2005 - an incident which saw Roy Carroll claw the ball back into play from well over the goal-line.
Redknapp said he rated Clattenburg as a referee despite what he deemed a catastrophic error, but may still find his incendiary comments scrutinised by the Football Association.
Asked if he had question the officials about the decision, he continued: "It's farcical, but what can you do? It's gone now.
"In the end he'll 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."