Wendy Martin's late, late goal rescued a 1-1 draw in normal time of this third round encounter.
Chances were few and far between in extra time and the game went down to the dreaded shoot-out that the home team won 4-2.
Manager Karen Hills reflected: "Credit to Larkhall, they deserved to go through to the next round.
"We had our chances to win the game in normal time but again we didn't take them and that has cost us a place in the next round."
There was a silver lining to a disappointing day, however, with the news that Keynsham beat Millwall in the FA Women's Premier League South, therefore guaranteeing the team's place in that division next season.
"That was our ultimate aim this season, so that's great news," added Karen.
Larkhall 1-1 Spurs Ladies (aet, Larkhall won 4-2 on penalties)
Spurs Ladies paid the price for failing to take their chances as Sunday's FA Women's Cup tie went to the wire.
Larkhall pressed well in the early exchanges as the team shook off the long journey to Bath and struggled to get their passing game going on a heavy playing surface.
Sam Pittuck slid a one-on-one opportunity wide and then both Sam and Bianca Baptiste fired in efforts from distance, to no avail.
Larkhall proved a tough nut to crack and then broke away to grab the lead just before half-time.
Spurs pushed for an equaliser in the second and camped in Larkhall's half. Kirsten Thompson, Robyn Downie and Robyn McEvoy all entered the fray but the home side managed to hold onto their lead.
That changed in the sixth minute of added time when Wendy Martin broke through, skipped around the goalkeeper and slotted home to take the game into extra time.
There were few chances in the extra half-hour, so it went to penalties with Larkhall coming through 4-2.
"We didn't play to our full potential, so that was disappointing," added Karen.
"But we have to put this behind us as soon as possible as we've League Cup group matches coming up against Watford and West Ham."
The team play the second and third matches in Group Two of the FA Women's Premier League's League Cup at Watford on Sunday before another away match, this time a midweek tie at West Ham on Wednesday, February 29.
Spurs Ladies: Jo Ayre, Miranda Hall, Vicky Elcome (Robyn McEvoy, 60), Ryha Vyse (Robyn Downie, 75), Wendy Martin, Jess Cheeseman, Jenna Schillaci, Emma Sherwood (Kirsten Thompson, 80), Sam Pittuck, Bianca Baptiste.