The Cumbrians let a 2-1 first leg advantage slip after losing 2-0 at home to Leeds on Thursday as they exited the play-offs at the semi-final stage.
Jonny Howson's last minute second cost Carlisle the chance of a final appearance at Wembley against either Doncaster Rovers or Southend.
"It's a small squad and that's probably cost us, but the desire and determination of this group of players is top drawer," said Ward.
"We didn't play as well as we did on Monday, but that's sport. Leeds did very well and I wish them well in the final.
"We have been in the top six all season and we've threatened big teams like this.
"That's pretty much my squad what you've seen out there tonight with three or four extra bodies, so we need to try and improve upon that but it has been a fantastic season."