Beckham said: "We knew if we kept on going we'd get chances and we'd put them away. We were a bit sluggish through the whole game but in the last five minutes we carried on and finished it off.
"The fans were great and cheered us on right to the end. You need that when it's 0-0 right to the end and we've done well tonight."
Asked whether the win had been vital to keep in touch with Arsenal, Beckham said:
"Arsenal are a great team. It's up to us and we are only interested in what we are doing. It's early season still. You don't want anyone at the top to get far away from you but we just want to concentrate on us at moment."