The Hammers are currently 16th in the Premier League, above the relegation zone on goal difference alone, while Crystal Palace are bottom with just three points from nine games.
A win for Palace could shake things up at the bottom end of the table, and goalkeeper Hart believes the match at Selhurst Park is their cup final.
The West Ham stopper told 'Sky Sports': "We've had wins, big wins, and not followed them up. Saturday is a humongous game, no matter what had happened at Wembley, Saturday is a huge game. We want to bring that second half form into Saturday.
"We're approaching it as the biggest game of the season. Crystal Palace are our cup final right now. We need to get some points on the board, and we need to get the group of fans behind us, who are struggling at the moment, and I understand why.
"That's the most important thing. Palace are probably having the same meetings, discussions as we are, they have the same feelings about the game as us. It's a huge, important game, and we need to be right.
"We want to be in games, in charge of games, and don't want to have to react, but we did what we had to do. But that was one of however many games we've had this season, and one of the highlights, but there has been a lot that hasn't been good enough."