Hitzlsperger surprised by reaction of fans
Hitzlsperger, 28, signed for the Hammers last summer, but injury has kept him sidelined until Monday, when he started the fifth round tie at Upton Park.
The Germany international grabbed the first goal with a trademark left-footed thunderbolt from the edge of the area and the Premier League strugglers went on to enjoy a confidence boosting win.
"I didn't know what to expect after such a long time out,'' Hitzlsperger told ESPN. "The manager was speaking to me before the game about whether I would play 30 minutes or start, but I'm delighted to start with a goal and an important win for us. It's going to bring some confidence back to the camp and that's important with the games ahead of us.''
"We knew that they're in good form in the Championship and we were well aware they would put pressure on us. They played well at stages but it was good timing for the goal and the fact I scored, it came together on a special day for me. It's been a tough time but I've been looking forward to this day and it was fantastic.''
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.''
Manager Avram Grant was happy to see his team show some good form and particularly enjoyed watching his players take on board the half-time advice to try to spring Burnley's offside trap more regularly.
"We are the Premier League team so normally we need to win these games, but they are difficult because they are playing well and tactically they are very good,'' he said. But we played well in the second half and it was difficult for them.''
"We spoke about this at half-time because the line of the defence was too high. "We passed the ball better in the second half and scored the goals.''
Grant admitted he would happily take three points over a cup win, but he is happy to continue a confidence-boosting run.
"Our target and first priority is the league, but it's always good to come into the quarter-finals of the cup,'' he said. "We want to win every game. We know in the cup you lose one game and you're out, but in the league there is always the next game to make things better.''
Burnley boss Eddie Howe felt his side gave a good account of themselves early on, but once they were 2-0 down, they let the game get away from them.
"I though it could have been very different,'' he said. "In the first half we had our moments, we had our chances and could have scored more than one. West Ham are dangerous up front with the pace they have and they caught us a couple of times.
"The goal straight after half-time hurt us and then we're chasing the game and they caught us on the break a couple of times.''