Tottenham's post-World Cup form had been disappointing, posting a 2-2 draw away at Brentford and losing 2-0 at home to Aston Villa over the weekend.
But Harry Kane's brace and goal each from Matt Doherty and Son Heung-Min ensured a comfortable night at Selhurst Park and ease some pressure that was slowly building on Conte.
Spurs have now closed the gap on fourth-placed Manchester United to two points and manner of the victory has provided Conte with some much-needed relief.
"There are moments when you need this type of performance," Conte told reporters after the game.
"It was important. Three points, [we] don't concede a goal. It wasn't easy. To play against Crystal Palace away is not easy. They beat us last season 3-0 [at Selhurst Park]. [It is] a really difficult pitch to play.
"I have many things to be happy about, especially for the young players. We are facing a difficult situation with injured players, especially. To see that you can count on them makes me happy. Also it's important because we can create competition."
Conte also lavished praise on Kane, whose brace took him to within two goals of Spurs' all-time top scorer Jimmy Greaves, who scored 248 times for the club.
"We are talking about a really world-class striker and he's going to beat that record with the goals," the former Chelsea boss added.
"For us he's an important point of reference. Especially in the moments you know Harry is there ready to fight and solve the situation with goals and assists.
"We have to continue in this way and face every situation, negative and positive, with great character.
"I hope that soon we can have the whole squad available and that will be very important to face Arsenal and Manchester City with all our players and then we can see our true level."
