Manchester United manager Louis van Gaal acknowledged his side was lucky to score in the last minute against Everton but deserved to reach the final of the FA Cup.
The Red Devils needed a late Anthony Martial to progress after Chris Smalling's own goal cancelled Marouane Fellaini's opening goal.
They will next face either Crystal Palace or Watford at Wembley on May 21.
"It's fantastic when you see the joy in the eyes of the players," van Gaal said.
"But also for the fans, because I think we deserved to reach the final. We were the better team in the first half and had so many chances - we could have finished it much earlier.
"It was an exciting game for the neutral fans and we are lucky that we scored in the last minute, but we deserved to win. I told [Chris] Smalling he was a lucky guy because now we can smile! He played a very good match. Both teams showed a lot of passion and will to win, so I'm very happy that we were the winners.
"He [Anthony Martial could have scored in the first half when he was in the same situation, so I told him at half-time to shoot low into the corner – and he did that! It was a fantastic finish.
"I think he can do much better [in the future] because I see a lot of things that he can still improve and he shall improve. Only by training and by playing can you improve. Also, when you are playing at a higher level then you improve. When you are older you know all the things shall happen again. Then you have experience and you can decide much better in the same situation as before."
