The hosts had the better of the first-leg clash at White Hart Lane, but it was the Serie A side who took a step closer to the last 16 courtesy of Jose Basanta's away goal, which cancelled out Roberto Soldado's early opener.
It was the first of six games in 17 days across three competitions for Tottenham and, while Pochettino was pleased with the display, the result left him unhappy.
"I think we deserved more," he told Spurs TV. "We created more chances in the first half and dominated the opening 45 minutes.
"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.
"They have a similar philosophy to us. We'll have another open game and try and reach the next round."
Pochettino will take his side to Italy for the second leg next week, just four days after a Premier League clash against West Ham and three before the League Cup final versus Chelsea.
The hectic schedule continues with league games against Swansea City and QPR the following week.
