Goals from Alexis Sanchez and Ander Herrera cancelled out Dele Alli's opener to send United into a third final in less than two years under Mourinho, having won the Europa League and League Cup last season.
Liverpool's 2-2 draw at West Brom in the Premier League also means United need just seven points from their remaining four league games to secure second place behind champions Manchester City.
United, Tottenham out to salvage season
"We should ask ourselves why there is too many critics on all of us?" said Mourinho. "We can finish second with seven more points. To do that with all the fantastic teams we play against will be an achievement for a club that couldn't do it for a few years now. We need two victories and one draw to finish second with 81 points behind an untouchable City, no chance to get in the fight with them. I think second with 81 points is a good season and then we can come to the final with a good spirit, supported by good supporters."
By contrast, a record eighth consecutive FA Cup semi-final defeat for Spurs ensured their decade-long wait for a trophy continues.
"We want to win trophies, we have the staff that want to win. We can't keep doing this," said Alli. "We can't throw it away. We have got to improve."
Spurs manager Mauricio Pochettino played down the importance of winning his first silverware as a coach beforehand, claiming it "wouldn't change their lives".
Manchester United face Pogba dilemma
And the Argentine insisted that finishing in the Premier League top four for a third consecutive season to qualify for the Champions League is more important to their progress as a club than silverware.
"For me the most important is now we finish in the top four to play again in the Champions League," said Pochettino. "Sometimes after the game I am very frustrated, but quickly I move on and we have four games to make sure we play Champions League. It will be a successful season if we assure our position."
Tottenham’s goalscorer Alli though was more frustrated than his manager. "We were dominant from the first minute and it only looked to be going one way," he added. "We let ourselves down, it's very disappointing."
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