The Premier County were appearing in their first ever All-Ireland decider yesterday and lost out to their Northern opponents on a full-time score of Tipperary 0-13 Tyrone 1-11.
Twomey questioned the referee's decision not to give Tipperary a free after sending off Tyrone's Michael Cassidy at the end the game.
He says his players will learn from the experience and will be back again next season.
Meanwhile Tyrone Manager Fergal Logan says the long half-time break may have played a role in their second half resurgence.
And there will be no homecoming for Tipperary's All-Ireland Finalists in Templemore today.
A function will be held at a later date instead.
