Asked if the 1-0 win ranked as his finest hour Redknapp said: "Yeah, it's a great day, I'm loving it.
"This was fantastic. We came here the other week and got slaughtered. This time we had a plan and we stuck with it. We grafted and we deserved it.
"You always have to ride your luck here. They are a fantastic team. No-one comes here without a bit of luck to win."
United should have been given the chance to open the scoring from the penalty spot on seven minutes, after Cristiano Ronaldo was crudely bundled over by defender Sylvain Distin.
However, Atkinson ignored United's appeals, prompting a furious response from Ferguson, who argued with the fourth official before exchanging words on the touchline with Portsmouth coach Joe Jordan.
Portsmouth, who lined up in a defensive 4-5-1 formation, found it difficult to put United under any pressure and their best first-half opportunity came when Croatian midfielder Niko Kranjcar saw his shot from 18 metres fumbled by keeper Edwin van der Sar.
United pay for missed chances
However despite dominating possession and field position, United failed to take their chances and Wayne Rooney wasted a golden chance to score on 19 minutes after being released by Ronaldo.
The England striker found himself one-on-one with keeper David James at the edge of the penalty area, but delayed his shot allowing defender Sol Campbell to make a crucial tackle.
Carlos Tevez picked up the loose ball and put a shot on target, only to see right back Glen Johnson head off the line.
The visitors continued to hold firm, and survived a real scare on 57 minutes when Nani's corner created three goal scoring opportunities for United.
Defender Nemanja Vidic's bullet header from Nani's cross was well-saved by James, but the loose ball fell to Tevez in the six yard box, but the Argentinian couldn't free himself to shoot on goal and his half-hearted effort was blocked.
The loose ball fell to Ronaldo on the edge of the penalty area, but the Portuguese winger couldn't add to his 30 goals already this season as he shot wide.
United's misses ultimately came back to haunt them on 78 minutes.
Anderson lost possession and Kusczak, on as a substitute for the injured van der Sar, hauled down Baros before being shown a straight red card.
Rio Ferdinand, United defender, donned the gloves and went into goal for the hosts, but Muntari's cool penalty gave the unlikely keeper no chance as Pompey moved within touching distance of their first FA Cup Final appearance since 1939.