Austin netted his second goal of the contest in the sixth minute of added-on time to send QPR to Wembley.
"It's been a fantastic night," Redknapp is quoted as saying by Sky Sports News. "They started well. I thought for 20 minutes they came out and we had problems with their system.
"We wanted to put pressure on but we couldn't get out, we didn't have an out ball. Then we went with two up front and I think the game changed then. From then on, I thought we were the better team.
"All round it was a great performance. We showed a lot of character, great character. Everybody dug in."
QPR will face Derby County in the final later this month, with a place in the Premier League up for grabs.