United had to bounce back after going a goal behind when Dele Alli gave Spurs an early lead, but Mourinho's charges responded through Alexis Sanchez and Ander Herrera to book their place in the final.
"The players were all very good and when they are all good the team is solid and we can play against any team including Spurs, who are one of the top teams in Europe," said Mourinho, according to BBC Sport.
"It was a great achievement to beat them in their stadium.
"I had this morning one simple SMS from one of my bosses Ed Woodward - he was saying that 'I believe we are going to win but if we don't the season is a good season, a season where everyone is professional and everyone is bringing the club in the right direction'. That's my feeling too.
"We can close the season in a final and that's a good achievement. But we need to focus on our six points and we deserve to finish second and to do that behind a fantastic team is a good achievement."
Mourinho has won the FA Cup once in his career, claiming the crown during the 2006-07 season with Chelsea.