A last-gasp strike from Anthony Martial sent Louis van Gaal's side through after a thrilling contest against an Everton side which had threatened to stage a remarkable comeback.
United dominated the first half and led through Marouane Fellaini's strike, only for the Toffees to fight back - missing a penalty through Romelu Lukaku before Chris Smalling's own goal drew Roberto Martinez's men level.
But Martial burst through in stoppage time to slot home and seal a memorable 2-1 victory for the 11-time winners, who have not lifted the cup since 2004.
Blind and his team-mates will now return for the showpiece final on May 21 but the Dutchman felt United made heavy weather of a contest they could have put to bed after a half of dominance.
"Our season is ending in London so that is nice," he said.
"In the first half we could have already finished the game. We had many chances, they had two as well to be honest, but I think we had to score more goals than today but I think it was a great game to see for the fans at the stadium.
"In the end it was going up and down and was very high tempo in the match and when there is only three minutes of injury-time then you think you are going to extra-time. Anthony scored a great goal and I can't describe the feeling."
Juan Mata is the only player in the current United ranks to have tasted FA Cup success, having played in the 2012 final for Chelsea as they beat Liverpool 2-1.
The likes of Wayne Rooney and Michael Carrick have tasted final defeat for the Red Devils, and the latter is now determined to add an FA Cup winners medal to his Premier League, Champions League, League Cup and World Club Cup successes.
"It would be amazing (to win the FA Cup), but I don't want to get carried away," he told MUTV.
"We've been to a final before and haven't won it, so the next game is even more important than this one.
"We'll enjoy tonight; it's a massive result and a great feeling but we'll start afresh in a few weeks' time.
"I can't remember the last time I had a feeling like that - it's a phenomenal feeling.
"It was a bit of a crazy game; we were very good in the first half and probably should have been further in front really. I know they had a couple of chances, but I think we dominated.
"It doesn't matter, though: we've come here and won and probably in the best way with a last-minute goal.
"We can go home absolutely delighted, but we're not getting carried away - we've still got a massive game to play in the final. We'll go home and concentrate on that."
For Everton, this was a missed opportunity to end a largely disappointing campaign with a Wembley final - with manager Roberto Martinez again questioned about his future after the loss.
Midfielder Tom Cleverley, a losing finalist with Aston Villa last season, praised the fans for their support and insists the players will now strive to end the season in better form.
"Things just haven't been going for us this season," he said.
"It's going to be a tough couple of days for us now but we can't feel too sorry for ourselves because we have to finish strongly in the league and then look towards next season.
"We were all fighting together as a club. The fans were magnificent and really got behind us even though we haven't been playing that well recently.
"They really sucked the ball down towards that end in the second half and, on any other day, it would have been an Everton win because we created the chances to do it."
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