The Elland Road club had trailed 2-1 after a disappointing first leg on Monday, but two goals from Jonny Howson at Brunton Park - the second in the final minute - secured their place at Wembley.
"It was a bit of a damp squib on Monday night at Elland Road, but I think the fans got the reaction they wanted," said McAllister.
"I'm very proud of the players and pleased for the players. Everything that's been put in front of them they've dealt with and I've not heard one murmur of complaint.
"We move on again. We're slightly closer to the Championship, but I don't want to be a killjoy as nothing's been achieved yet.
"We've still got to go and try and win a game at Wembley."
Leeds will play either Doncaster Rovers or Southend United in the final.