Sherrock, 70, was granted the opportunity to appear as a Premier League “challenger” after reaching the last 32 at the Alexandra Palace in December.
None of the previous 13 “challengers” had won their games and Sherrock fell just short of more darting history.
She told Sky Sports: “I’ve loved every minute. I’m so happy to have played again on the big stage. I’m speechless and I’d like to thank everyone here supporting me.
“Opportunities are opening up for me all the time and I can’t wait to see what the rest of 2020 holds for me. ”
Durrant added: “The crowd were fantastic, it was a really big challenge and all credit to Fallon.
” She’s had the most amazing couple of months . That’s the most difficult match I’ve ever had. “
A group of nine” challengers “play one match each against a player in the main field in the first phase of the Premier League and, while they do not collect league points, they can earn prize money depending on their result.
The format was introduced in after Gary Anderson pulled out of the event at short notice with a back injury, and has been continued into the tournament.
Defending champion Michael van Gerwen is the only player with a 561% winning record after two rounds of fixtures, following a crushing 7-1 win over Daryl Gurney.
Former PDC world champion Rob Cross was the only other winner on Thursday, defeating in-form Nathan Aspinall 7-5.
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