Keothavong suffered disappointment in the singles and doubles
Great Britain missed out on a place in the Fed Cup World Group II play-offs after losing 2-1 to Poland.
Things got off to a winning start when Elena Baltacha beat Katarzyna Piter 6-4 6-1 in the opening singles match.
Then, Anne Keothavong lost a tense match 7-6 7-6 against world number nine Agnieszka Radwanska to set up a doubles rubber to decide the match.
Keothavong and Sarah Borwell took on Klaudia Jans and Alicja Rosolska, with the Poles winning 7-5 6-3.
"This time last year we narrowly avoided relegation, this year we came very close to going up so I'm really proud of all the girls' efforts," said GB captain Nigel Sears.
"I really couldn't have asked them to give any more this week.
"It's heartbreaking to come so close, the girls played superbly in their singles matches today and we just weren't quite good enough to win the doubles rubber."
After edging a tense first set, Baltacha claimed two breaks of serve early in the second to gain the upper hand on the inexperienced Pole.
She then held her nerve, despite the distraction of a noisy crowd supporting hosts Estonia against Belarus on the neighbouring court, to win and give Great Britain an early advantage.
In the next match, Keothavong and Radwanska each managed three breaks of serve in the opening set before the Pole won the tie-break.
The second set was a fraught affair, with Radwanska claiming the first break in the seventh game and then holding her serve to go 5-3 up.
Keothavong held her serve to force Radwanska to serve for the match, which she failed to do, and the set ended up going to a tie-break again.
But despite a heated debate towards the end of it, Radwanska kept her cool to win the match 7-6 7-6, setting up the doubles decider.
Keothavong and Borwell broke their more experienced opponents in the fifth game but Borwell was broken back to level the set at 4-4, and another break in the 12th game gave the Poles the opening set.
They followed this up by racing to a 5-0 lead in the second set, and despite a mini-revival including saving three match points, the British duo lost it 6-3, and with it the match and the overall tie.