The game against Chelsea or Liverpool will be the first all-English final in the history of the competition.
United, who were without injured duo Wayne Rooney and Nemanja Vidic, were under pressure for long spells but their defence ensured Barca had very few clearcut chances.
"It's not easy to beat Barca because they play fantastic football but several things won us the game," said Ferguson.
"The concentration at the back, we protected the space really well and with our play up front, we could have scored three or four goals.
"I think we were too nervous in the first half but in the second half we played with much more conviction.
"Towards the end of the game, they had a go and we're very glad we got through that spell in the last 15 minutes. It was a bit of a 'hang-on job' but they didn't really make any chances and that's down to our defence."
Captain Rio Ferdinand was among United's best players, along with defensive partner Wes Brown, midfielder Ji-Sung Park and the tireless Carlos Tevez.
Ferdinand said: "We had to dig deep at the end because they put us under pressure.
"It was our discipline and a moment of quality from a fantastic player that got us through. We don't care who we play in the final. Whoever comes we will be ready."
Barcelona coach Frank Rijkaard admitted his side's inability to turn possession into chances had cost them.
"We did everything but score," he said.
"It was a very even game, if anything we had the better of the play. But the rules are that the team that scores goes through and they did that.
"It is a tough defeat to take and it is hard to stomach. The Champions League is very important and it is over for us now. But after this game can walk away with our heads held high."
• Paul Scholes has a mark of 7.88 for Tuesday's game in the BBC's Player Rater, trailing team-mates Carlos Tevez (8.49), Rio Ferdinand (8.05) and Wes Brown (8.01). Lionel Messi is comfortably Barcelona's top man, with a mark of 8.25.
You can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
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