Roberto Soldado gave the hosts a dream start when he volleyed home a corner in the sixth minute but Jose Maria Basanta's equaliser secured Fiorentina a draw and a crucial away goal.
The Italians will be favourites to make the last 16 ahead of next week's return leg, particularly as Tottenham may have one eye on their Capital One Cup final against Chelsea three days later.
"It is a shame because at half-time we deserved to have scored more than one goal but it was only 1-1," Pochettino said.
"We need to go to Florence and win the game and score
Today we were better than Fiorentina, especially in the first-half.
"We created a lot of chances but this is football
I think in the first half we controlled the game but we had more of the ball in the second half.
"In general, over the 90 minutes we were better
We had the chances, the possession of the ball and managed the game."
Pochettino added: "It's a shame and I'm disappointed with the result because I think we deserved more, but I'm happy with the performance."
Pochettino opted to rest the likes of Harry Kane, Ryan Mason and Mousa Dembele against Fiorentina as Spurs enter a pivotal period that includes six games in 17 days.
Tottenham are sixth in the Barclays Premier League, only three points off the top four, and Pochettino admits he will have to juggle the team's league and cup commitments in the coming weeks.
"Both competitions - the league and the Europa League - can give us access to the Champions League," Pochettino said.
"We are fighting for the Europa League and in the Premier League
We try to focus on the next game and not think too much about the future."
Pochettino added: "We need to make decisions because we have a lot of games coming up, six games in 17 days.
"It's difficult and we need to rotate, give everyone the possibility to play.
"It's not difficult to pick the starting 11, I try to select the best team to win the games."
Fiorentina boss Vincenzo Montella felt his team finished the stronger side and looked more likely to win the game in the second half.
"It was a fair result
In the first 30 minutes we suffered a bit because of their high tempo and physical game, but we knew that was going to happen," Montella said.
"I also think they paid the price in the second half for all the energy they expended.
"In the second half we turned things around and could perhaps have scored a second goal.
"It was a fair result and the return leg will be a very open game."
Source : PA
Source: PA