Coventry goalkeeper Sue Wood kept Spurs at bay as they racked up over 20 efforts at goal without reward at Cheshunt FC.
Spurs included new signings Megan Wynne and Kelley Blanchflower - Wynne, a Welsh international striker formerly with Watford in Women's Super League 2, started while Blanchflower, a forward snapped up from West Ham, came on in the second half.
"The first half was even but we dominated the second half," reported manager, Karen Hills.
"We ended up with 22 efforts at goal, we just couldn't get that elusive goal. We did everything right.
"We always knew it would be a tough game but with the chances we had, we're disappointed not to take the three points. But there were lots of positives for us."
Spurs travel to QPR in the FAWPL on Sunday (2pm).
Spurs Ladies: Chloe Morgan, Lucia Leon (Rosie Kmita), Sophie McLean (Kelley Blanchflower), Alex Keown, Leah Rawle, Shannon Moloney, Megan Wynne (Jenny Moore), Mia Vio, Bianca Baptiste (c), Katie O'Leary, Avilla Bergin. Substitutes (not used): Mollie Kmita, Wendy Martin.