The Teessiders missed the chance to step up to Premier League after losing 2-0 to the Canaries in the play-off final at Wembley on Monday after first-half goals from Cameron Jerome and Nathan Redmond.
"It is difficult because this team has done everything this season to get promotion but football is football," Karanka told Sky Sports.
"We beat them twice but today they were better. They didn't make mistakes. We made two mistakes and in a final you pay for those mistakes.
"I think we have to be proud of the players and of this crowd. For me it is amazing to be here. It is not our moment now. We were not ready."