Isn't that the worst feeling. I did something similar last year when I installed a high quality (translated: high cost) laminate floor in my living area. Before I was even finished laying the laminate I moved the couch from the unfinished side of the floor to the finished side of the floor. When I slid the couch there must have been a tack or nail under one of the legs because I got a nice deep, long gouge in of the floor. If I hadn't been gluing the pieces in, I would have undone everything and replaced those panels.
In your case, you might want to think about taking out the panel that is damaged and installing a new one. This can be done without removing the entire floor, but it isn't easy. When I was looking into it (see above mishap) I decided not to bother with it since the damaged area is covered with a rug anyway. If I recall correctly the process involves using a circular saw )set to the correct depth) to cut out the existing damaged board. Then you remove the interlocking joint material from the new panel with a saw and set the new panel into the hole where the damaged panel was removed. You'll need to use glue to hold it in place since there won't be any interlocking.
If the damaged piece is close to one of the long edges of your room, it might be easier to remove the flooring up to that point and replace the panel that way.