Spurs took the lead at White Hart Lane when Soldado fired in a volley after only six minutes.
But Fiorentina equalised later on in the first half through defender Jose Maria Basanta.
This gives them the crucial away goal.
Spurs visit Florence for the return leg in a week’s time.
Mauricio Pochettino said after the game:
They have a similar philosophy to us. We’ll have another open game and try and reach the next round. I’m happy with the performance but disappointed with the result. We need to go to Florence to try and win the game and progress. I think we deserved more. We created more chances in the first half and dominated the opening 45 minutes.