Chelsea overcame their London rivals 4-2 in the FA Cup London derby after late goals from Eden Hazard and Nemanja Matic sent the Blues into the final where they will face either Arsenal or Manchester City.
Spurs made Chelsea's life difficult, however, as Harry Kane and Dele Alli twice brought the north Londoners back from trailing positions to threaten to send the game to extra-time.
But after Conte's substitutions proved decisive, Chelsea secured a win in a game the Italian was proud to have been part of.
He said after the victory: "To reach in my first season a final is a great achievement but not only for me, but for my players, the club, the staff and our supporters.
"We deserved this after a tough game with a strong team.
"To see this type of game, England must be proud to have this game with these level of players and intensity. It was a great show for football.
"It was a semi-final with two teams very strong and a really good game, not only for Chelsea but also Tottenham."
The performance from the Chelsea players was a marked improvement from how they played at Old Trafford last Sunday when Manchester United comfortably defeated the league leaders 2-0.
With tough Premier League games against Southampton and Everton to come in the next seven days, Conte urged his players to use the momentum from their win over Spurs to help them over the line in the race for the top-flight trophy.
"This week is crucial for us," he said.
"They (Spurs) have the advantage and we have to play after two-and-half days [against Southampton on Tuesday].
"Spurs have a day more rest than [Crystal] Palace. We must exploit the momentum."