Spurs, who lost 3-1 at rivals Arsenal in the Premier League on Saturday, had plenty of opportunities through Harry Kane, Son Heung-min and Ivan Perisic, especially in the first half, but have now gone seven European away matches without a win.
Europa League winners Eintracht and Spurs are both on four points from three matches, with Sporting in the top spot on six despite their 4-1 loss at bottom club Olympique de Marseille, who have three points.
"It was a good match. We played with great intensity," said Tottenham coach Antonio Conte. "I think we need to be more clinical. We created many, many chances to score. It's not easy to play away with this atmosphere, I think my players coped with that well.
"In football, you have to score. I think for the big effort for the whole team maybe we deserved much more. The most important thing for me is to create chances.
"There are moments you are more clinical, there are moments like in the game against Arsenal and today you create chances but make a mistake with the last pass," he said.
In an entertaining first half, Tottenham's intensity was up from their London derby defeat and Kane had two chances in quick succession, narrowly failing to connect with Son's inswinging delivery in the 27th and then firing just wide a minute later.
Perisic could have done better when his shot also missed the mark as Spurs lacked efficiency with their finishing.
The Germans, in their maiden Champions League campaign, remained solid at the back and had a golden opportunity through Ansgar Knauff but goalkeeper Hugo Lloris made a diving save.
Lloris became only the second French keeper to record more than 20 clean sheets in the Champions League by joining Fabien Barthez on 21.
Tottenham and Frankfurt meet again next Wednesday in London.