The Hammers will face Stoke in the next round, but Hitzlsperger also hopes the win can spur them on in the league, as they remain 19th in the table.
"This is what we needed, I think, especially by such a great margin," he said. "5-1 is a good win for us. With the games we have coming up, we're playing some really good teams so we need confidence and structure in our game.
"We can't make any mistakes because we need to climb up the table."