The Hammers went into the game at Wembley under pressure after losing their last Premier League game to Brighton.
Boss Slaven Bilic is close to the sack according to some sections of the media, but he got a response from his players as they reached the quarter-final of the Carabao Cup, coming from two goals down to defeat Tottenham 3-2.
Andre Ayew grabbed a brace before Angelo Ogbonna scored the winner and Lanzini insists the team head to Crystal Palace in good spirits.
He told the club's official website: "I hope it's the turning point of the season. These games, beyond winning them, give you an enormous morale boost.
"Obviously, it was important for us because it wasn't just a big match but a derby, and you always have to win derbies. But hey, we have to continue this way. We know that we have to play like this, with this desire, with this attitude. We have great players and we want to continue this way."