The Bees will take on either Huddersfield or Carlisle at Wembley after Myles Weston set up goals for Sam Saunders and Gary Alexander to see them through 3-2 on aggregate.
Forster, put in charge after Andy Scott was sacked last week, said: "I don't think we started with the tempo or the intensity that I would have wanted.
"But as soon as we got Myles into the game - and he had the chance to attack the full-back - we caused problems and we knew we would if we got crosses into the box.
"I think we were worthy winners, I really do.
"Myles Weston has been fantastic. When he has that confidence and belief and really gets at people with conviction and positivity, then he is a difficult player to mark. He can be our spark and he proved that."