Marcello Trotta's last-minute penalty miss on the final day of the season cost the Bees the chance to go up to the Championship automatically.
They needed another late spot-kick from captain Kevin O'Connor to salvage a 1-1 draw at Swindon in the first leg of their play-off semi-final, and recovered from conceding an injury-time equaliser to win on penalties following Monday's 3-3 second-leg thriller at Griffin Park.
Moore, who saved Miles Storey's penalty in the shoot-out, admitted: "You couldn't write it.
"A penalty against Doncaster, a penalty at Swindon in the last game and a penalty on Monday. Penalties are a cruel thing but we have felt the elation that can come with it. We deserve it after the disappointments we have had this season.
"It sums up our season really. It's been unbelievable with so many highs and lows.
"Monday proved the team spirit we have here is unbelievable and we will take that confidence to Wembley and hopefully finish the job.
"I felt so confident. I love penalty shoot-outs and I knew that I would save at least one. The boys' penalties were absolutely brilliant.
"The amount of pressure that was on them and they were so cool. We are all buzzing but we will bring ourselves back down to finish the job off in a couple of weeks."