"We were all a little disappointed after the game because we felt like we should have won," Cork told the club's website. (www.swansea city.net)
"We had a good first half and in the second half it was always going to be difficult as the away side."
Bradley, who admitted that he was still searching for his strongest team, made eight changes to the side that lost 3-1 at home to Manchester United in their last match, and was rewarded by an improved performance, if not all three points.
Cork said the display on Merseyside had given Swansea the belief they could get a first win for Bradley when they host 16th-placed Crystal Palace, whose 2-1 home defeat by Manchester City on Saturday was their fifth league loss in a row.
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"Hopefully this can be a bit of a kickstart for us this season," the 27-year-old added.
"We have the big home game against Crystal Palace next week and hopefully we can get going.
"We have to stick together now and work hard in the next game, just as we did against Everton. Hopefully then the rewards will come."
Sigurdsson said Swansea desperately needed a win against Palace to pull themselves out of their slump and took heart from the fact the team looked like they were finally starting to gel under American Bradley's stewardship.
"It's a huge game for us and we need to build on this point today and hopefully go on a run because we need the points desperately," the Iceland international said.
"If we play like we did in the first half we will be fine -- defensively we were rock solid, and going forward we looked dangerous."
(Reporting by Debanjan Bose in Bengaluru; Editing by John O'Brien)
