After seeing Costa and Hazard fail to make an impact in Chelsea's 2-0 loss to Manchester United on Sunday, Conte made the big call to start Michy Batshuayi up front against Spurs and Willian on the flank.
The move paid off as Willian netted a free kick and then a penalty while Batshuayi forced Hugo Lloris into a save from his fine header in the first half.
But with Spurs scoring twice to level the game at 2-2, which threatened to take the tie into extra-time, Conte reactd by bringing on Costa, Hazard and Cesc Fabregas.
Costa didn't get on the scoresheet, but Hazard and Fabregas combined for both of Chelsea's late goals that secured a 4-2 win over Tottenham and sends the Blues into the FA Cup final.
After the match, Conte admitted he had taken a big risk by dropping his star players and, indeed, playing Natan Ake in defence over John Terry or Kurt Zouma but insisted he had faith his squad players would make the difference.
"When you arrive in this part of the season and you know you have to play three tough games in a week, one against a top team - this game was top of our priority - but then play on Tuesday after just three days and against a team who have 10 days of rest, you must take strong decisions and take the responsibility also," he said.
"It's not easy to decide to start without two really players in Eden and Diego. You must take this risk. I'm pleased because Michy started this game and it was important for him and for his confidence - like Ake.
"He's from our academy and we must be proud. To see his commitment and his level, it's not easy for Ake to go and play in this game. But I trust them and every single player. Today, I showed this."
When then asked about Willian, who has spent much of this season acting as a substitute, Conte replied: "I'm pleased for Willian because he showed himself to be in good form and this season it wasn't easy for many reasons.
"I involved all my players in our idea and our football and that's important in this part of the season. It's important every single player feels part of his project.
"When you try and involve every player in your idea and you call on them then they are ready to fight and play."